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# 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.

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This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
This is an important ques and asked in 1992

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.
Question no. 14 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

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1. Solution:

Given:

Length of garden = 16cm

Width = 10cm

Let the width of walk be ‘x’ meter

Outer length = 16 + 2x

Outer width = 10 + 2x

So according to the question,

(16 + 2x) (10 + 2x) – 16(10) = 120

160 + 32x + 20x + 4x2 – 160 – 120 = 0

4x2 + 52x – 120 = 0

Divide by 4, we get

x2 + 13x – 30 = 0

x2 + 15x – 2x – 30 = 0

x(x + 15) – 2 (x + 15) = 0

(x + 15) (x – 2) = 0

So,

(x + 15) = 0 or (x – 2) = 0

x = -15 or x = 2

∴ Value of x is 2 [Since, -15 is a negative value]

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