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# A rectangular lawn has dimensions of 24 ft by 32 ft. A sidewalk will be constructed along the inside of all four sides. The remaining lawn will have an area

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A rectangular lawn has dimensions of 24 ft by 32 ft. A sidewalk will be constructed along the inside of all four sides. The remaining lawn will have an area of 425 square ft. How wide is the walk? Please show your work

Guest Mar 2, 2017
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A rectangular lawn has dimensions of 24 ft by 32 ft. A sidewalk will be constructed along the inside of all four sides. The remaining lawn will have an area of 425 square ft. How wide is the walk? Please show your work

Assuming that the sidewalk has a uniform width......call the width, x

And we have that

(24 - 2x) (32 - 2x) = 425    simplify

4x^2 - 112x + 768 = 425

4x^2 - 112x + 343  = 0  factor

(2x - 7) (2x - 49)  = 0       set each factor to 0

2x - 7   = 0                                2x - 49   =  0

2x = 7                                       2x =  49        divide both sides by 2

x = 7/2 ft  = 3.5 ft                        x = 49/2  ft  = 24.5 ft

24.5 ft sounds pretty wide for a sidewalk!!!......besides......it's an impossible answer

3.5  ft. seems more reasonable.....

CPhill  Mar 2, 2017

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