SOLUTION: This was under the conic section of my book but I am not sure if it is a review or if it is really a conic section problem. It seems really simple but after I looked at it for a w

Question 10295: This was under the conic section of my book but I am not sure if it is a review or if it is really a conic section problem. It seems really simple but after I looked at it for a while I realized I didn't know what to do.
Find the dimentions of a rectangle that has the area of 10 and a dioganal length of 5.

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = width of the rectangle
y = length of the rectangle
5 = diagonal of the rectangle

By the Theorem of Pythagoras,
By the way, this equation would be the equation of a circle, which is probably why this problem is in your conic section section of the book!!

Solve for y:

Area = xy = 10

Square both sides:

Set the equation equal to zero by taking everything to the right side of the equation, in order to get the x^4 to have a positive coefficient.

It doesn't always happen, but it sure feels good when it does--that math comes out even! This does indeed factor!!

It turns out that if , then and if , then . So there is actually only one solution. The rectangle is by .

R^2 at SCC
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