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) (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
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