Question 282462
How do I solve the story problem that states, "find the dimensions of a rectangle that has area 10 and a diagonal of length 5. leave your answer in terms of radicals."

Let L be the length and W the width.  Then the area = L*W = 10 and L = 10/W.

By the Pythagorean Theorem we have for the triangle created by the diagonal:

W^2 + (10/W)^2 = 5^2

W^2 + 100/W^2 = 25
w^4 + 100 = 25W^2
W^4 - 25W^2 + 100 = 0
(W^2-20)*(W^2-5) = 0

W=sqrt(20) = 2*sqrt(5)
 or
W=sqrt(5) 

Calculate L = 10/W.