SOLUTION: A walking path of uniform width is to be built along all four sides of a rectangular courtyard that measures 15 yards by 8 yards. If the total area covered by the courtyard and the

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Question 908076: A walking path of uniform width is to be built along all four sides of a rectangular courtyard that measures 15 yards by 8 yards. If the total area covered by the courtyard and the walking path, combined, is 260 square yards, what is the width of the walking path?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width be x
..
Length of courtyard 15 yards
width of courtyard 8 yards

Area = 120 sq. yards
Area of plot 260 sq. yards
length of courtyard & plot 15 + 2 x
width of courtyard & plot 8 + 2 x

( 15 + 2 x ) ( 8 + 2 x ) + 0 = 260

120 + 30 x + 16 x + 4 X^2 + 0 = 260
4X^2 + 46 x + -140 = 0 /2
2x^2+23x-70=0
2x^2+28x-5x-70=0
2x(x-14)-5(x-14)=0
(2x-5)(x-14)=0
x=5/2 OR 14
14 is not applicable
Hence width = 2.5 yards