# algebra

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?

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1. 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

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