Question 196132
The distance between two opposite corners of the pool is about 1590 ft. The length is about 1325 ft. longer than the width. What are the length and width of the pool?
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Because the pool is rectangular you can apply Pythagorean theorem:
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Let w = width
then
w+1325 = length
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w^2 + (w+1325)^2 = 1590^2
w^2 + (w+1325)(w+1325) = 1590^2
w^2 + (w^2+2650w+1755625) = 2528100
2w^2 + 2650w + 1755625 = 2528100
2w^2 + 2650w - 772475 = 0
Solving using the quadratic equation yields:
w = {245.87, -1570.87}
We can throw out the negative solution leaving:
w = 245.87 feet (width)
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length:
w+1325 = 245.87+1325 = 1570.87 feet (length)
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Details of quadratic follows:
*[invoke quadratic "w", 2, 2650, -772475 ]