SOLUTION: So I received this question, and have no clue how to answer it: 2 legs of a right triangle are in the ratio 5:6. The hypotenuse is 2 radical 61 meters long. If the longer of the

Algebra ->  Pythagorean-theorem -> SOLUTION: So I received this question, and have no clue how to answer it: 2 legs of a right triangle are in the ratio 5:6. The hypotenuse is 2 radical 61 meters long. If the longer of the      Log On


   

Question 921845: So I received this question, and have no clue how to answer it:
2 legs of a right triangle are in the ratio 5:6. The hypotenuse is 2 radical 61 meters long. If the longer of the two legs is doubled and the shorter remains the same, what is the length of the new hypotenuse. I don't even really want an answer, but just steps in the right direction. Thanks
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The original triangle analyzed:
Let x be some positive real number.
USING Pythagorean Theorem formula, %285x%29%5E2%2B%286x%29%5E2=%282sqrt%2861%29%29%5E2, and you can solve this for x.

STEPS TO FIND x.
25x%5E2%2B36x%5E2=2%2A2%2A61
61x%5E2=4%2A61
x%5E2=4
highlight%28x=2%29

The next part gives new conditions and a question.
The original triangle's legs are 5%2A2=10, and 6%2A2=12.

The side 12 is to be doubled, meaning becomes 24; and the side 10 remains unchanged. Find the new hypotenuse!