A rectangular garden 10 m by 16 m is to be surrounded by a concrete wa

1.	A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniformwidth. Given that the area of the walk is 120 square metres, assuming the width of thewalk to be x, form an equation in x and solve it to find the value of x.
Answer» Length of the rectangular garden = 16 m Breadth of the rectangular garden = 10 m Area of the rectangular garden = 1610 = 160 m² Area of the concrete path of width x meters (given) = 120 m² Total area = area of rectangular garden + area of the path ⇒ 160 + 120 = 280 m² The width of the concrete path is uniform (Given) So, Length of the whole rectangle (including concrete path) = (16 + 2x) m Breadth of the whole rectangle (including concrete path) = (10 + 2x) m ⇒ (16 + 2x)(10 + 2x) = 280 ⇒ 4x² + 52x + 160 = 280 ⇒ 4x² + 52x + 160 - 280 = 0 ⇒ 4x² + 52x - 120 = 0 ⇒ Dividing the whole equation by 4, we get. ⇒ x² + 13x - 30 = 0 ⇒ x² + 15x - 2x - 30 = 0 ⇒ x(x + 15) - 2(x + 15) = 0 ⇒ (x - 2) (x + 15) = 0 ⇒ x = 2 or x = - 15 As the width cannot be negative. So, the value of x is 2 x = 2 m Length of the outer rectangle = 16 + (22) = 20 mBreadth of the outer rectangle = 10 + (22) = 14 m

A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniformwidth. Given that the area of the walk is 120 square metres, assuming the width of thewalk to be x, form an equation in x and solve it to find the value of x.

Answer»

Length of the rectangular garden = 16 m

Breadth of the rectangular garden = 10 m

Area of the rectangular garden = 16*10

= 160 m²

Area of the concrete path of width x meters (given) = 120 m²

Total area = area of rectangular garden + area of the path

⇒ 160 + 120

= 280 m²

The width of the concrete path is uniform (Given)

So,

Length of the whole rectangle (including concrete path) = (16 + 2x) m

Breadth of the whole rectangle (including concrete path) = (10 + 2x) m

⇒ (16 + 2x)*(10 + 2x) = 280

⇒ 4x² + 52x + 160 = 280

⇒ 4x² + 52x + 160 - 280 = 0

⇒ 4x² + 52x - 120 = 0

⇒ Dividing the whole equation by 4, we get.

⇒ x² + 13x - 30 = 0

⇒ x² + 15x - 2x - 30 = 0

⇒ x(x + 15) - 2(x + 15) = 0

⇒ (x - 2) (x + 15) = 0

⇒ x = 2 or x = - 15

As the width cannot be negative. So, the value of x is 2

x = 2 m

Length of the outer rectangle = 16 + (2*2) = 20 mBreadth of the outer rectangle = 10 + (2*2) = 14 m