SOLUTION: A rectangle with an area of 60 square feet has a diagonal of 13 feet. find the sides of the rectangle. this is for roots but we can use any method ancient or modern. I know x

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Question 839982: A rectangle with an area of 60 square feet has a diagonal of 13 feet. find the sides of the rectangle.
this is for roots but we can use any method ancient or modern.
I know xy=60 and x^2 + y^2=13^2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle with an area of 60 square feet has a diagonal of 13 feet. find the sides of the rectangle.
this is for roots but we can use any method ancient or modern.
I know xy=60 and x^2 + y^2=13^2
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y = 60/x
x%5E2+%2B+%2860%2Fx%29%5E2+=+169
x%5E2+%2B+3600%2Fx%5E2+=+169
x%5E4+%2B+3600+=+169x%5E2
x%5E4+-+169x%5E2+%2B+3600+=+0
Sub u for x^2
u%5E2+-+169u+%2B+3600+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-169x%2B3600+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-169%29%5E2-4%2A1%2A3600=14161.

Discriminant d=14161 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--169%2B-sqrt%28+14161+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-169%29%2Bsqrt%28+14161+%29%29%2F2%5C1+=+144
x%5B2%5D+=+%28-%28-169%29-sqrt%28+14161+%29%29%2F2%5C1+=+25

Quadratic expression 1x%5E2%2B-169x%2B3600 can be factored:
1x%5E2%2B-169x%2B3600+=+%28x-144%29%2A%28x-25%29
Again, the answer is: 144, 25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-169%2Ax%2B3600+%29

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y%5E2+=+144
x = 12
y = 5
or vice versa