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Question
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Solution
Length of garden = 16 m
and width = 10 m
Let the width of walk = x m
Outer length = 16 + 2x
and outer width = 10 + 2x
Now according to the condition,
(16 + 2x)(10 + 2x) -16 x 10 = 120
⇒ 160 + 32x + 20x + 4x2 - 160 = 120
⇒ 4x2 + 52x - 120 = 0
⇒ x2 + 13x - 30 = 0 ...(Dividing by 4)
⇒ x2 + 15 x - 2x - 30 = 0
⇒ x(x + 15) -2(x + 15) = 0
⇒ (x + 15)(x - 2) = 0
EIther x + 15 = 0,
then x = -15
But it is not possible.
or
x - 2 = 0,
then x = 2.
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