SOLUTION: A rectangle has a diagonal measuring 13 feet and its area is 60 ft^2. What are its dimensions?

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Question 600385: A rectangle has a diagonal measuring 13 feet and its area is 60 ft^2. What are its dimensions?
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
let the rectangle's length = L and rectangle's width = W
L%2AW+=+60%2C+so+L+=+60%2FW

L%5E2+%2B+W%5E2+=+13%5E2
%2860%2FW%29%5E2+%2B+W%5E2+=+169
3600%2FW%5E2+%2B+W%5E2+=+169
multiply all by W%5E2
3600+%2B+W%5E4+=+169W%5E2
W%5E4+-+169W%5E2+%2B+3600+=+0
Factorize it into:
%28W%5E2+-+144%29%2A%28W%5E2+-+25%29+=+0
W%5E2+-+144+=+0+or+W%5E2+-+25+=+0
W%5E2+=+144 or W%5E2+=+25
W=12 or W=-12 or W+=5 or W=-5
because the dimension of a rectangle can't be negative numbers, so
W = 12 or W = 5
if W = 12 then L = 60/12 = 5
if W = 5 then L = 60/5 = 12

so the dimension of the rectangle is 12 ft x 5 ft