# Geometry

Henry has a patio next to his house that is 15ft by 10ft. He wants to put a uniform flower bed around three sides of the patio. The area of the flower bed is 100 ft^2. What is the width of the flower bed?

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1. Is it 6.67 ft

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2. let the width of the uniform border be x ft
new width = 10+2x
new length = 15 + 2x

area of whole thing = (10+2x)(15+2x)
(10+2x)(15+2x) - 150 = 100
150 + 50x + 4x^2 - 15 - 100 = 0
4x^2 + 50x - 100 = 0
2x^2 + 25x - 50 = 0

doesn't factor, so use the formula
x = (-25 ± √1025)/4
= 1.754 or some negative

So 1.754 ft must be added to the width and length, so the width of the flower bed must be 1.754 ft

check:
area of patio = 150 ft^2
area of whole thing
= (10+2(1.754)) (15+2(1.754))
= 249.999.. or 250

increase = 250 - 150 = 100

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posted by Reiny

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