Question

The length and width of a rectangular garden are 150m and 120m. a foot path of regular width is added to the boundary of the garden and the total area of the garden becomes 2800m2 more than its original area. find the width of the footpath.

Answer 1

Hi friend,

Here is your answer,
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Let the width of path be x.
Length of garden with path = 150 + 2x
Width of garden with path = 120 + 2x

Original area of park = 120*150
Area of park with path = (150+2x)(120+2x)

              (150+2x)(120+2x)  -  150*120         =  2800m²
=> 150*120 + 300x + 240x + 4x² - 150*120  =  2800
=>                                          4x²  +  540x     =  2800
=>                                4x² + 540x - 2800      =  0 
=>                                  x² + 135x - 700        = 0
=>                          x² + 140x - 5x - 700         = 0 
=>                            (x+140)(x-5)                  = 0
=>     x = -140       OR           x = 5

∵ length can not be -ve 
∴ we will accept x = 5m

Width of footpath = 5m
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