Question

A rectangular garden 10m by 16m is to be surrounded by a cincrete walk of uniform width.Given that area of the walk is 120 square metre, find its width

Answer 1

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

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