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Quadratic Equations in One Variable | Quadratic Equations in One Variable Exercise 5.5

Question 14

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 meters, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x. (1992)

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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

\begin{array}{l} 160+32 x+20 x+4 x^{2}-160-120=0 \\ 4 x^{2}+52 x-120=0 \end{array}

Divide by 4, we get

\begin{array}{l} x^{2}+13 x-30=0 \\ x^{2}+15 x-2 x-30=0 \end{array}

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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Question 14

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 meters, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x. (1992)

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

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

\begin{array}{l} 160+32 x+20 x+4 x^{2}-160-120=0 \\ 4 x^{2}+52 x-120=0 \end{array}

Divide by 4, we get

\begin{array}{l} x^{2}+13 x-30=0 \\ x^{2}+15 x-2 x-30=0 \end{array}

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]

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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