The length and width of a rectangular garden are 150m and 120m respectively. A footpath of a regular width is added to the boundary of the garden. With this the total area becomes $2800 m^{2}$ more than its original area. Find the width of the footpath.

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Solution

Original length =150m
Original breadth = 120m Area = $150 \times 120$
= $18000 m^{2}$
Let the width of foot parts be x.
New length = 150+2x New breadth = 120+2x
New Area = (150+2x)(120+2x)
Given, (150+2x) (120+2x) = 2800+18000
18000+240x+300x+4x2 = 2800+18000
$4 x^{2} + 540 x - 2800 = 0$
$x^{2} + 135 x - 700 = 0$
(x+140)(x-5)=0
x=5, -140
x=5m

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The length and width of a rectangular garden are 150m and 120m respectively. A footpath of a regular width is added to the boundary of the garden. With this the total area becomes 2800m2 more than its original area. Find the width of the footpath.

The length and width of a rectangular garden are 150m and 120m respectively. A footpath of a regular width is added to the boundary of the garden. With this the total area becomes $2800 m^{2}$ more than its original area. Find the width of the footpath.