the-area-of-a-right-triangle-is-6sqrt2-square-centimeters-and-the-length-of-one-leg-is-sqrt12-cenime

Question

The area of a right triangle is 6$\sqrt{2}$ square centimeters and the length of one leg is $\sqrt{12}$ cenimeters.
What is the length of the other leg?
What is the length of the hypotenuse?

Matt Gibson · Accepted 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.

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

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.

Gianna Calciano · Answer

to solve this problem, we need to use the Pythagorean theorem. So we know that the high pot new squared is equal to the sum of the two legs squared. We then get three X weird is equal to 1 44 Next, we can divide the 1 44 by three. We get X weird is equal to 48 and X is equal to the square root of 48. Condemn, plug this into our area equation and doing so we can simplify the square root of 48 as well. We&#x27;ll get our friend on answer to be 24 birth three.

Nick Johnson · Answer

all that the lengths of the legs of an assassin. Please strangle our X and the square root of six X plus 16. Well, and I assassinates triangle, right. These sides are going to be equal so we can go ahead and set these things equal can set X equal to the square root of six X plus 16 and then find out what X is. Whatever exes is gonna be the length off the legs here. So solving this equation well, we can go ahead and can square both sides to just eliminate this radical the square root. So squaring both sides gives us X squared is equal to just what&#x27;s underneath the radical, namely six x plus 16 then can go ahead and we can subtract these terms to the other side toe. Have a quadratic in standard form that steady course zero. So we&#x27;re gonna get we have an X squared and then subtracting six x gives us a negative six x it&#x27;s attracting 16 gives us minus 16 which is then equal to zero. So we have a quadratic write in standard form people. Zero. Can we go ahead and factor this? Let&#x27;s try it so we try and factor this quadratic well, we haven&#x27;t X Square that has the X Times X 16. What&#x27;s eight times two was different is six. So if we have an eight and a too, any different signs that multiply to a negative 16 and adding to a native sex meaning the negative but it be on the eight on the plus on the two, we have X minus eight times X plus two equal to zero, which would mean right that either X minus two or X plus two will be equal to zero, which would imply that X would be DiPoto AIDS or X would be equal to negative two. But wait a minute. This is a side we&#x27;re finding here is the side of this triangle is it makes sense to have a side that&#x27;s a negative length, right? You check both of these answers, and they could both in a check out. But you can&#x27;t have a lings right to be equal to a negative number. So you go ahead and we throw out X equal to negative two, and we do that exited. Just because a plug in eight year we ate is equal to the square root of six times eight plus 16 while six times eight is 48 plus 16 is, um, 64 right in the square isn&#x27;t before is eight. So it checks out at eight. Is equal to need. Right, Which checks out. So therefore, our solution here is X equals eight. If when I read this as what&#x27;s the solution set while it&#x27;s the set containing it. So the solution set here is 88 is the side of the triangle. All right, take your

Dilip Paruchuri · Answer

all right. Hey, guys. So when this problem, we&#x27;re getting a triangle. We&#x27;re told that the longer side has a length of of 20 feet. The shorter has outside has a length of 12 feet and were asked to find the length of the high pot news. So this is a simple, basically plug and chug Pythagorean theorem problem. So what we&#x27;re going to do is going to write the Pythagorean theorem we&#x27;re gonna say are by their in the erm is a squared. Plus B squared is equal to C squared, where a and B are the lengths of our legs and seize the high pot in use. So let&#x27;s plug it. So we&#x27;ll say 12 squared plus 20 squared is equal to C squared. We know 12 squared is equal to 1 44 20 squared is equal to 400 so 1 44 plus 400 is equal to C squared. So we&#x27;re saying that 5 44 is equal to C squared. Now we want to get the sea by itself because that&#x27;s the value of our high pot news. So what we do, we take the square root of both sides. So the problem boils down to us. Simplifying 544 square root of 544. So 544 doesn&#x27;t look like a square or cube. So the next best thing if you don&#x27;t recognize that number, is a square or cube, the best thing to do is to fact arises. We&#x27;ll draw factor, diagram or factor tree. So let&#x27;s go start simple. We know that 5 44 is even so let&#x27;s divide out by two. And when you divide out by two, you get 2 72 and then we can also we also see that to 72 is. Even so, we could divide out by two once again and then we get that 12 times 1 36 is equal to 2 72 We see that 1 36 is also even. So we see that Toronto to we get a 68. You could factor another tomb and you get that 68 is equal to two times 34. Finally, the last factories ation you get up slips right out of its smaller. So you get that 34 is equal to two time 17. The factory ization of 45 54 is equal to 12345 It&#x27;s gonna be equal to two to the fifth times seven teen. And when you take the So basically, now what we&#x27;re doing is we&#x27;re taking the square root of two to the fifth time 17 and clearly we&#x27;re not going to get a perfect rash of perfect real number. We&#x27;re gonna have an irrational part. We&#x27;re gonna have a radical part. Our goal now is to play around with these numbers. So we get a radical part and a real number part. So what I&#x27;m gonna do is I&#x27;m going to rewrite our two to the fifth as two squared squared times two times 17 now to two square square. This part is equal to two to the fourth. Two to the fourth times two times 17 is the same thing as to the fifth time 17. And now this step, we&#x27;re gonna break apart into two radicals. So we&#x27;re gonna break apart into a multiplication of radicals. So we know that this step is equal to two square square times two times 17. When you do something the square root of something squared, you just get that something so square root of to school. The quantity of two squared Claire is just equal to two squared, two squared and square root of two times 17 is just equal to square root. 34. Now, if we write this better, our answer is going to be four times Square Root 34. And that&#x27;s what our value of Cy&#x27;s gonna be and seize our high pot news. So our high potting uses four times Radical 34. Thank you for listening, guys, and I hope there&#x27;s helped just to recap. This was a simple by that Dorian Theorem problem. And when we solved, we saw that we got the square. We gotta square root of a number. That&#x27;s not a perfect square. So we had to draw factor free diagram and we had to play around with numbers so we could simplify it into a real part multiplied by a radical part are real part Here is four radical part here is next square with a 34. Uh, thanks for listening, guys. And I hope this helps

Problem 31 Hard Difficulty

The area of a right triangle is 6$\sqrt{2}$ square centimeters and the length of one leg is $\sqrt{12}$ cenimeters.
What is the length of the other leg?
What is the length of the hypotenuse?

Answer

a) 2$\sqrt{6} \mathrm{cm}$
b) 6 $\mathrm{cm}$

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Algebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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a) 2$\sqrt{6} \mathrm{cm}$b) 6 $\mathrm{cm}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

a) 2$\sqrt{6} \mathrm{cm}$
b) 6 $\mathrm{cm}$

Ann Xavier Gantert

Algebra 2 and Trigonometry