Answer to Question 4
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When determining the expressions to represent the sides of the pool, be sure to subtract the sidewalk width twice - once from each side of the pool. 24 - 2x and 41 - 2x |
Since we know the "area" of the pool, let's start with area.
The area of the pool can be expressed as:
(24 - 2x)(41 - 2x) = 630
984 - 48x - 82x + 4x2 = 630
4x2 - 130x + 354 =0 (factor or quadratic formula)
2x2 - 65x + 177 = 0
(2x - 59)(x - 3) = 0
2x - 59 = 0; x = 29.5 ft (not realistic sidewalk width)
x - 3 = 0; x = 3 feet (acceptable sidewalk width)
The area of the pool can be expressed as:
(24 - 2x)(41 - 2x) = 630
984 - 48x - 82x + 4x2 = 630
4x2 - 130x + 354 =0 (factor or quadratic formula)
2x2 - 65x + 177 = 0
(2x - 59)(x - 3) = 0
2x - 59 = 0; x = 29.5 ft (not realistic sidewalk width)
x - 3 = 0; x = 3 feet (acceptable sidewalk width)
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