A rectangle has a length that is 5 feet more than its width. The area of this rectangle is 84 square feet. What is the width and length of this rectangle?
L = Length
W = Width
A = Area
L = W + 5
A = W * L
84 = W * ( W + 5 )
84 = W ^ 2 + 5 W
W ^ 2 + 5 W = 84 Add 25 / 4 to both sides
W ^ 2 + 5 W + 25 / 4 = 84 + 25 / 4
W ^ 2 + 5 W + 25 / 4 = 336 / 4 + 25 / 4
W ^ 2 + 5 W + 25 / 4 = 361 / 4
( W + 5 / 2 ) ^ 2 = 361 / 4
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Becouse:
( W + 5 / 2 ) ^ 2 =
W ^ 2 + 2 * W * 5 / 2 + ( 5 / 2 ) ^ 2 =
W ^ 2 + 5 W + 5 / 4
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( W + 5 / 2 ) ^ 2 = 361 / 4
W + 5 / 2 = + OR - sqrt ( 361 / 4 )
W + 5 / 2 = + OR - 19 / 2
1 case :
W + 5 / 2 = 19 / 2 Substract 5 / 2 to both sides
W + 5 / 2 - 5 / 2 = 19 / 2 - 5 / 2
W = 14 / 2 = 7 ft
2 case :
W + 5 / 2 = - 19 / 2 Substract 5 / 2 to both sides
W + 5 / 2 - 5 / 2 = - 19 / 2 - 5 / 2
W = - 24 / 2 = - 12 ft
Width can't be negative, so:
W = 7 ft
L = W + 5 = 12 ft
A = W * L = 7 * 12 = 84 ft ^ 2