A lawn is 14m x 10m. Round the lawn there is a gravel walk. The area of the lawn is 7/9 that of the gravel walk. Find the width of the walk
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Answer:
6m
Step-by-step explanation:
area of lawn = 14*10 m
According to the question,
area of lawn = 7/9 * area of gravel walk
14*10*9/7 = area of gravel walk
area of gravel walk = 180
(14 + x)*(10 + x) - (14*10) = 180
x² + 24x + 140 - 140 = 180
x² + 24x - 180 = 0
x² + 30x -6x - 180 = 0
x (x + 30) - 6 (x + 30) = 0
(x + 30)(x - 6) = 0
x = -30 or 6
Since the width cannot be negative,
Thus the width of the gravel walk is 6 m.
Hope this helps . . . also comment if further doubt.
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