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."

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) (Show Source): You can put this solution on YOUR website!
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.

RELATED QUESTIONS
Find the dimensions of a rectangle that has an area 48 m^2 and a diagonal of length 10... (answered by Earlsdon)

Please help me find the dimensions of a rectangle that has an area of 10 and a diagonal... (answered by venugopalramana)

I dont understand how to solve a problem that states : Find the area of a rectangle with... (answered by Earlsdon)

Ok, there is a problem in my worksheet that gives me the following information:... (answered by scott8148,ankor@dixie-net.com)

Find the dimensions that produce the maximum floor area for a one-story house that is... (answered by LinnW)

how do I find the area of a rectangle that has a perimeter=72 & width =16? (answered by Fombitz)

How do I set up this story problem? The width of a rectangle is three-fifths the length. (answered by QH)

a rectangle has area 100 ft^2. Find the dimensions of the rectangle that would minimize... (answered by Fombitz)

The area of a rectangle is 12sq. units and the diagonal of the rectangle has a length of... (answered by ankor@dixie-net.com)