SOLUTION: 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."

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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."
Answer by dabanfield(803) About Me  (Show Source):
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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.