SOLUTION: he diagonal of a rectangular storage room is 8 yards long. if its length is 2 times its width, find the dimensions of the room

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Question 544073: he diagonal of a rectangular storage room is 8 yards long. if its length is 2 times its width, find the dimensions of the room
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2%2Bb%5E2=c%5E2
a=length
b=width
c=diagnal
if a=2b and c=8 then solve for b
a%5E2%2Bb%5E2=c%5E2
%282b%29%5E2%2Bb%5E2=%288%29%5E2
4b%5E2%2Bb%5E2=64
5b%5E2=64
b%5E2=%2864%2F5%29
sqrt%28b%5E2%29=sqrt%2864%2F5%29
b=sqrt%2864%29%2Fsqrt%285%29
highlight%28b=8%2Fsqrt%285%29%29
a=2b
a=2%288%2Fsqrt%285%29%29
highlight%28a=16%2Fsqrt%285%29%29
check
a%5E2%2Bb%5E2=c%5E2
%2816%2Fsqrt%285%29%29%5E2%2B%288%2Fsqrt%285%29%29%5E2=8%5E2
%28256%2F5%29%2B%2864%2F5%29=64
256%2B64=320
320=320
Correct