SOLUTION: A rectangular pool has dimensions of 40 ft. and 60 ft. If the pool has a patio around it that equals the area, how wide is the distance from the pool edge to the patio edge?

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Question 192753: A rectangular pool has dimensions of 40 ft. and 60 ft. If the pool has a patio around it that equals the area, how wide is the distance from the pool edge to the patio edge?

I can't figure out how I would represent this. Would you please help? Quadratic equations really perplex me. Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming the width of the patio around the pool to be uniform, let's call this x.
The total area of the pool plus patio can be expressed as:
A%5Bt%5D+=+%2840%2B2x%29%2860%2B2x%29 and this is twice the area of the pool alone A%5Bp%5D which means: 2%2AA%5Bp%5D+=+2%2860%29%2840%29 = 2%2A2400+=+4800, so...
%2840%2B2x%29%2860%2B2x%29+=+4800 Multiply and rearrange into standard form:
4x%5E2%2B200x%2B2400+=+4800 Divide through by 4 to simplify a bit.
x%5E2%2B50x%2B600+=+1200 Subtract 1200 from both sides.
x%5E2%2B50x-600+=+0 Factor this quadratic equation.
%28x-10%29%28x%2B60%29+=+0 Apply the zero product rule.
x-10+=+0 or x%2B60+=+0 so...
x+=+10 or x+=+-60 Discard the negative solution 'cause widths are positive quantities.
highlight%28x+=+10%29
The patio is 10 feet wide.