A rectangular garden 10 m by 16 m is 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 m, form an equation in x and solve it to find the value of x.

Question

KnowledgeBoat · Accepted Answer

Let ABCD be a rectangular garden.

Let the width of the walk be x m

ABCD is the rectangular garden,

Length of rectangular garden = 16 m

Breadth of rectangular garden = 10 m

From figure,

Length of PQRS = 16 + x + x = (16 + 2x) m

Breadth of PQRS = 10 + x + x = (10 + 2x) m

Area of PQRS = (16 + 2x)(10 + 2x)

Area of rectangular garden ABCD = 16 × 10 = 160 m²

Area of concrete walk = 120

Now,

From figure,

⇒ Area of walk = Area of rectangle PQRS - Area of rectangle ABCD

⇒ (16 + 2x)(10 + 2x) - 160 = 120

⇒ (16 + 2x)(10 + 2x) = 120 + 160

⇒ (16 + 2x)(10 + 2x) = 280

⇒ 160 + 32x + 20x + 4x² = 280

⇒ 4x² + 52x + 160 = 280

⇒ 4x² + 52x + 160 - 280 = 0

⇒ 4x² + 52x - 120 = 0

⇒ 4(x² + 13x - 30) = 0

⇒ x² + 13x - 30 = 0

⇒ x² + 15x - 2x - 30 = 0

⇒ x(x + 15) - 2(x + 15) = 0

⇒ (x - 2)(x + 15) = 0

⇒ (x - 2) = 0 or (x + 15) = 0

⇒ x = 2 or x = -15

Since width cannot be negative,

x = 2 m.

Hence, the width of the concrete walk is 2 m.

Mathematics