the-length-of-one-leg-of-an-isosceles-right-triangle-is-6-inches-express-the-length-of-the-hypotenus

Name: the length of one leg of an isosceles right triangle is 6 inches express the length of the hypotenus
Uploaded: 2019-07-31
Duration: 1 min 13 s
Channel: Numerade
Description: The length of one leg of an isosceles right triangle is 6 inches. Express the length of the hypotenuse in simplest radical form.

Question

The length of one leg of an isosceles right triangle is 6 inches. Express the length of the hypotenuse in simplest radical form.

Finian Lickona · Accepted 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

Matt Gibson · Answer

I always like to draw a picture for a problem like this. So I&#x27;m giving one side of my right triangle, and I&#x27;m trying to find the height. So if I know the area, my formula is areas 1/2 base times height. I would substitute the area in for a I&#x27;m giving one side. So I plugged it in for B and I&#x27;m trying to find the height by multiply both sides by two. I can reduce here and this on the left side, I&#x27;m left with 12 times the square to two on the right side. I&#x27;m left with the square to 12 times H divide both sides by this word of 12 leaves me with on the left side I can reduce the squared of two and this word of 12 to make my number smaller. So that would wind up giving me that slide up here That would give me 12. Divided by this word of six equals h. I can&#x27;t leave a radical in the denominator. Some going to rationalize that the nominator by multiplying the top and bottom by the squared of six and I multiply by one. It doesn&#x27;t change the value which has changed what it looks like. So I have 12 times a squared of six, divided by the square root of 36 which is just six, and I would equal my height. Finally, I can reduce the six goes into 12 twice, and I get two times. The square of six equals my height. Finally, I&#x27;m asked to find the length of the high pod news. I&#x27;ll call that. See if my H is too times this word of six. I can use the Pythagorean theorem and I can say two times a squared of six squared. Plus, the square root of 12 squared equals C squared so that the factory theorem is a squared plus B squared equals C squared, where a and B are the two legs. If I square the squared of 12 that&#x27;s easy. That just gives me 12 when I square two times this word of six to swear it is four. This word of six times it&#x27;s where two sixes, the sweat of 36 which is just six, and I would equal C Square, so four times six gives me 24 plus 12 gives me C squared 36 seat will c squared. Take the square root of both sides and I know it can&#x27;t be a negative because it&#x27;s a side of a triangle, so I get six equals.

Nick Johnson · 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.

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.

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.

Ankit Gupta · Answer

it is given that triangle ABC is an isis less right angled drinking. Now we need to find the hyper tennis in terms off as we&#x27;re s sista side off the isis less triangle ABC Now, by using fighter goes to Adam, we have bc scare is equal toe a be scared plus sc scared. Now we can draw here that off diagram off Isis less right angle triangle were These two sides are equal and these are equal toe s and this represent the hyper tennis off the right angle triangle. Now we have We&#x27;re putting the valley off BC&#x27;s ical toe edge and we&#x27;re putting the value of a B and a C physical toe s we have at the scary will equal toe access to power two plus as s arrest of our two, which is equal to at a list of our two is equal to two s rest of power to. So from here, the value off H is equal toe scared off to ask for a raise to power to which is equal toe scare it off to multiplied with s So this is over. Answer

Problem

The length of the hypotenuse of a right triangle …

Problem 40 Hard Difficulty

The length of one leg of an isosceles right triangle is 6 inches. Express the length of the hypotenuse in simplest radical form.

Answer

6$\sqrt{2}$

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6$\sqrt{2}$

Algebra 2 and Trigonometry

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Algebra 2 and Trigonometry