SOLUTION: a rectangle has a width 5 feet shorter than the length. the area of the rectangle is 14 square feet. what is the length of the rectangle

Question 930420: a rectangle has a width 5 feet shorter than the length. the area of the rectangle is 14 square feet. what is the length of the rectangle
Found 2 solutions by algebrahouse.com, ewatrrr:
Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
x = length
x - 5 = width {width is 5 shorter than length}

Area of a rectangle is length x width

x(x + 5) = 14 {substituted width and length into area of rectangle}
x� + 5x = 14 {used distributive property}
x� + 5x - 14 = 0 {subtracted 14 from each side}
(x + 7)(x - 2) = 0 {factored into two binomials}
x + 7 = 0 or x - 2 = 0 {set each factor equal to 0}
x = - 7 or x = 2 {solved each equation for x}
x = 2 {length cannot be negative}

length is 2 ft

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Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
.
A = Lw
L(L-5) = 14 ft^2
F First terms
O Outside terms + I Inside terms = -5
L Last terms
L^2 - 5L- 14 = 0 (tossing out negative solution for unit measure)
(L+ 2 )(L - 7) = 0
L = 7ft and w = 2ft
and...checking
A = (7ft)(2ft) = 14 ft^2
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