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.

A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. The area of concrete walk is 120 square metre.

Assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.

Answer 1

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 × 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.