the-lengths-of-the-legs-of-a-right-triangle-are-8-centimeters-and-12-centimeters-express-the-length-

Name: the lengths of the legs of a right triangle are 8 centimeters and 12 centimeters express the length
Uploaded: 2020-08-14
Duration: 2 min 15 s
Channel: Numerade
Description: The lengths of the legs of a right triangle are 8 centimeters and 12 centimeters. Express the length of the hypotenuse in simplest radical form.

Question

The lengths of the legs of a right triangle are 8 centimeters and 12 centimeters. Express the length of the hypotenuse in simplest radical form.

Nick Johnson · Accepted Answer

given here the lengths of the legs of a right triangle are 87 years in 12 centimeters. Okay, so here&#x27;s a right triangle. Here&#x27;s our two legs. Seven the length of the iPod news. Well, we know that by Pythagorean theorem, right that we know that eight squared plus 12 square is going to be equal to of this length. We call it Let&#x27;s call it art cortex. So it&#x27;s equal to while X squared. So I&#x27;m a square. That&#x27;s gonna be 64 right? So you have 64 plus 12 square is going to be 100 and 44 so we have 64 plus 144 is equal to X squared. So therefore so what is 64 plus 144 is gonna be equal. Teoh 208. So we have 208 is equal to X squared. So what is Exe Um that&#x27;s where it acts. 208 is equal. Oops. It is equal to X squared. OK, so 208 is equal to X squared. That means that X is gonna be equal to the square root of 208. Okay, so now I want to go ahead and try and simplify. This is the square root of 208. Is there a perfect square? Such that that number times itself is gonna be equal to 200 eat? Um, let&#x27;s see. 200 aids is 16. Yes, 16 times 13 is actually 208. So we have exited equal to the square root off while 16 times 13. But the square 16 is four. That can come outside of your square root. So therefore, this is equal to four times the square root of 13. There&#x27;s no answer. And of course, this is in well, centimeters, right? So he here is our answer. All right, take care.

Nick Johnson · Answer

here&#x27;s triangle. I&#x27;m given that the length of the high pat news is, what, 24 meters in length of one legs of this right triangle is 12 meters. So how we find this other length? Let&#x27;s just go ahead is called this length. Um, you goto x meters that we know that well, 12 squared plus X squared right is gonna be equal to 24 square. So we have that, um while 12 times 12 that&#x27;s 144. So we have 100 and 44 plus X squared is equal to 24 squared, which I believe is that C 576. Okay, so then we&#x27;ll X squared is equal to 5 76 minus 1 44 which is 4 32 So we have that X squared is equal to 432 which means square root of both sides. That X is equal to the square root of 432. Okay, it&#x27;s not a try and simplify this or 432. Um hmm. Is there a perfect square such that that perfect square times it is gonna be time, something is going to be equal to 432 um 4 32 divided by who was 1 44? Yeah, 1 44 times three is actually 4 32 So here X is equal to the square root of 4 32 is actually 144 times three. But this word of 1 44 is 12. That 12 can come outside your radical before this is equal to 12 times the square root of three. Of course, this is this is in meter. All right, so the other side of the triangle is 12 times to score 23 meters.

Finian Lickona · Answer

So in this problem, we are given that the leg of a right I saw sleaze triangle is six inches, so that means that the other leg is also six inches by the definition of a nice Oslo. He&#x27;s trying, and if we remember our price, thuggery and serum of a squared plus B squared equals C squared. The square of the two legs equals the sum of the square. The two legs equals C square of the high pot names, so this leg is six, so that&#x27;s going to be 36 plus 36 equals C squared. So if we want to actually get the length of the iPod news, we&#x27;re gonna have to take the square root of both of these terms. And we can rewrite this as the radical of two times 36 equals the length of the iPod, the length of the high pot news. So 36 is obviously a perfect square. We can factor that outside of the radical. So are high pot. Innis length is actually going to be six times a radical, too, because the two cannot be brought outside of the radical

Meredith Moody · Answer

So in order to solve this problem with my right triangle, I&#x27;m going Teoh have to put my values in the factory and Europe because this is a right triangle. So we&#x27;re going to be using the Pythagorean theorem, which I have up here. And I know my shortest side, which I have chosen to the A is the base model here, like this is the one that we know. So I&#x27;m just going to use a for a so a square, and then this would be my, uh might be like so I&#x27;m gonna say might be is the shortest leg plus four millimeters So a squared plus B squared. So this is b squared equals C, which is the high pot news. So my C is actually the short leg plus eight millimeters put by the way, that&#x27;s what these little things are down here. There, there, there, abs for millimeters on. And so, when I put my value in for see, I have a plus eight square s so I have to do some foiling. And so I need Teoh right out my, uh, parentheses Here. A plus four square is April&#x27;s four times a plus four and then I have a must eight square. So I&#x27;m going Teoh, right, shapeless. Eat that. Now I&#x27;m going to multiply out my parentheses so eight times a of a square. That&#x27;s the outer. Or that&#x27;s the first terms. Thea Outer terms eight times four is for a inner terms. Eight times fours for a last terms four times four is 16 and same thing with my see value here eight times a a squared first terms outer terms is eight times eight. So that&#x27;s eight a inner terms is eight times eight, that&#x27;s a and my last terms are eight times eight, which is 64. Now I&#x27;m going to combine some like terms here My a swears I&#x27;m gonna dio that&#x27;s gonna be to a squared I&#x27;m gonna combine my A&#x27;s here. So I have eight a and then I just have plus 16 And then over here I have one a squared and then I&#x27;m gonna combine my A&#x27;s over here. So plus state 16 A and then plus 64. So now I have an equation with two quadratic on either side of the equal sign, so I am going to start moving some things around so that I can have everything on one side. So I&#x27;m gonna subtract my a squared from both sides, and that&#x27;s gonna leave me with simply one a square. Um, and I&#x27;m gonna have I&#x27;m only gonna do one step at a time, just so I don&#x27;t increase the likelihood of making mistakes which happened so that I&#x27;m gonna go with my A term and this subtract my A term from both sides, and that&#x27;s gonna give me a squared. Plus, I&#x27;m not gonna have a negative eight. A plus 16 equals 64. And then, of course, I can subtract 64 from both sides, and that is gonna leave me with a squared plus negative A plus. I have a negative. Um, yeah, that&#x27;s gonna be 64. 54 48. I can subtract. Negative. 48. Okay. All right. On. That&#x27;s now gonna equal zero, because that&#x27;s gone. And so now I can factor. I can factor. My polynomial actually been factored over. Here s oh, I have a square plus actually do minus minus. A minus 48 equals zero. So I know I&#x27;m gonna have my two parentheses here, so I&#x27;m gonna have because my life. See, term is negative or it&#x27;s this attraction. I know my factors. One of them is gonna be edition, and the other is gonna be surprised. And because my, um a term my ex square term is has a coefficient of one. I&#x27;m simply gonna have eight times a. So now all I have to do is I have to figure out which factors of 48 when I combined them, give me negative ate leftover sauna. I&#x27;m going Teoh factor this. So two times. Three to tax for two times two. All right, so I have two times, Two times, Two times. Two times three. All right, so I just have to figure out how to combine these so that when I subtract, um, I have eight as my difference. So, um, two times, two times two is eight. And the neck, it&#x27;s he says, Okay, so eight minus six doesn&#x27;t get me eight, but, um, this would be two times this would be 16 minus three. That doesn&#x27;t give it to me either. Or so six times two is 12. Oh, here we go. All right. So this is four times three is 12 and then two times two is four. So if I do four times 12 I get 48. But if I dio four minus 12 I get negative eight. That&#x27;s exactly what I need to dio. So my 12 has to be in the subtraction because I have to have eight negatives leftover, and my four has to be in. My pluses are my at addition Now I&#x27;m gonna set these equal to zero each one equal to zero and solve for my variable Some this attract for here this attract for here where I&#x27;m left with a equals negative for Well, that doesn&#x27;t really make a whole lot of sense, because we&#x27;re talking about a triangle and you can&#x27;t have negative cycling, so I&#x27;m going to do a minus 12 equals zero. So I get to add 12 both sides, and that leaves me with a equals 12. And so since my shortest leg is 12 millimeters now go back up. I&#x27;m also gonna turn off my into shape so I don&#x27;t end up with weird shapes all over the place. Uh, now I can determine my other sidelines as well. So since the a side, like the short side length is 12 b is then going to be 12 plus four, which is 16. So be is 16 millimeters. I should probably do that in red. Here we go. 16 millimeters and my high pot news see is my A Value plus eight on DSO See is 20 millimeters, so we have short whenever a is 12 millimeters be 16 millimeters and C is 20 millimeters.

Emily Burns · Answer

if we have a nice sauce Elise, Right? Triangle. That means that our to silence A and B are the same measure to a label. That s so, uh, you know that the Pythagorean theorem works for all right triangles. In this case, since our A and B are the same length, we can then change this be to a second A which means we have to a squared equals C squared were given that R. C is eight. So we have eight squared is equal to to a squared. We can then whoops because then square this have 64 is equal to two a squared divide both sides by two So then we&#x27;ll have 32 is equal to a squared Take the square root of both of thes And from there you can find your measure of each side. So we&#x27;ve got the square root of 32 which is five point 656 is equal to a so we can run that to the nearest 10th just to keep it simple. So we&#x27;ve got five point you&#x27;ve got our temps waste. Look to the right that numbers of five or higher you bring it up one. So we&#x27;ve got 5.7 as our measure for both our side nights

Ankit Gupta · Answer

in a right angle triangle. It is given that the hypertension is equal toe six centimeter, and we have to find the other two legs off the right angle triangle. Let ex and why be the other two legs off the right angle triangle Now, According to caution, one leg is one centimeter more than two times off the first, Let no since the given triangle is a right angle triangle, so we can apply here by total serum, according to which hypertension scare is equal to base a scare plus perpendicular skill. Now, by putting the values off hypertension and the other two legs, we have six. A scare is equal to exit scare plus two weeks plus once whole skill. Now, by solving this, we have excess care. Plus four excess care plus one plus four X is equal to 36. Now by simplifying it, do we have access care? Five. Excess care plus for X minus 35 is equal to zero now, by comparing it with standard quadratic equation, we have the value of a is equal to five. The value of B is equal to fall on the Valley. Off C is equal to minus 35. Now for finding disc imminent, we have be scared minus four a. C. Now we&#x27;re putting the value of A B and C. We have four scare minus four multiplied with five my deployed with minus 35. Now, by solving this, we have the value 716 Now, by using quadratic formula, the value of X will be minus B plus minus. Scared off this crimen int upon to eight. Now, by putting the value of B, D and E, we have minus four plus minus scared off 716 upon to my d played with fight. Now, since the length cannot be negative, so we have to take only the post to value that is minus four plus 716 a bone. Gen No. The scare it off 716 is equal to 26.75 So our answer will be 2.27 which is approximate is equal to 2.3. Now, By putting the value of facts invite we have, why is equal to two my deployed with 2.27 plus one that is equal to 5.54 which is approximate is equal toe 5.5 70 meters, so the other two legs are two point trees and Tim it&#x27;ll and 5.5 centimeters.

Problem

The length of one leg of an isosceles right trian…

Problem 39 Hard Difficulty

The lengths of the legs of a right triangle are 8 centimeters and 12 centimeters. Express the length of the hypotenuse in simplest radical form.

Answer

4$\sqrt{13}$

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4$\sqrt{13}$

Algebra 2 and Trigonometry

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Algebra 2 and Trigonometry