SOLUTION: The hypotenuse of a right triangle is twice as long as one of the legs. If the other leg is the square root of 8, find the other leg. So I thought the problem would be set up as x^

Algebra ->  Pythagorean-theorem -> SOLUTION: The hypotenuse of a right triangle is twice as long as one of the legs. If the other leg is the square root of 8, find the other leg. So I thought the problem would be set up as x^      Log On


   



Question 1083771: The hypotenuse of a right triangle is twice as long as one of the legs. If the other leg is the square root of 8, find the other leg. So I thought the problem would be set up as x^2 + square root of eight squared = 2x squared. but the answer after I work the problem is not correct. Please help! My second day on this problem!
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The hypotenuse of a right triangle is twice as long as one of the legs. If the other leg is the square root of 8, find the other leg. So I thought the problem would be set up as x^2 + square root of eight squared = 2x squared. but the answer after I work the problem is not correct.
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1 side = sqrt(8)
Other side = a
c = 2a
---
c^2 = a^2 + 8
(2a)^2 = a^2 + 8
4a^2 = a^2 + 8
3a^2 = 8
a^2 = 8/3
a+=+sqrt%288%2F3%29+=+2sqrt%286%29%2F3

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the hypotenuse be c,legs a and b

in a right triangle: c%5E2=a%5E2%2Bb%5E2
if the hypotenuse c of a right triangle is+twice+as long as one of the legs, let’s say a, we have c=2a->a=c%2F2
if the other leg b=sqrt%288%29, than we have:

c%5E2=%28c%2F2%29%5E2%2B%28sqrt%288%29%29%5E2

c%5E2=c%5E2%2F4%2B8

c%5E2-c%5E2%2F4=8

3c%5E2%2F4=8

3c%5E2=8%2A4

c%5E2=32%2F3

c=sqrt%2832%2F3%29

c=3.265986323710904

c=3.27

->a=c%2F2->a=3.27%2F2->highlight%28a=1.64%29->other leg

b=sqrt%288%29->b=2.83

check:
c%5E2=a%5E2%2Bb%5E2
%283.27%29%5E2=%281.64%29%5E2%2B%282.83%29%5E2
10.6929=2.6896%2B8.0089
10.6929=10.6985.........round to one decimal place
10.7=10.7