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Q.

A rectangular garden 10m by 16m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square meters assuming the width of the walk to be x, find the value of x?

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a

5

b

4

c

3

d

2

answer is D.

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Detailed Solution

https://www.vedantu.com/question-sets/f36e8545-356e-4766-8583-87ccb5a61d16486233308379381230.png

Area of walk = Area of outside rectangle - Area of inside rectangle

120 = (10 + 2 x) (16 + 2 x) - (10) (16)

120 = 160 + 20 x + 32 x + 4 x^{2} - 160

4 x^{2} + 52 x - 120 = 0

x^{2} + 13 x - 30 = 0

x^{2} + 15 x - 2 x - 30 = 0

x (x + 15) - 2 (x + 15) = 0

(x + 15) (x - 2) = 0

x = - 15 or x = 2

Since width cannot be negative

\to x = 2

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A rectangular garden 10m by 16m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square meters assuming the width of the walk to be x, find the value of x?