Question

Length of a rectangular garden is
10m and its breadth is 8 m if a road of
Uniform width of x m is surrounded
outside the park find the area of the road in terms of x​

Answer 1

Area of surrounded road = (4x² + 36x) m²

First find the area of the rectangular garden

Length of a rectangular garden = 10 m

Breadth of the rectangular garden = 8 m

Area of the rectangular garden = 10 m * 8 m

= 80 m²

So, Area of rectangular garden = 80 m²

Find Area of the rectangular garden including surrounded uniform width

Road surrounded with uniform width = x m

Length of the rectangular garden including surrounded uniform width = 10 + x + x = (10 + 2x) m

Breadth of the rectangular garden including surrounded uniform width = 8 + x + x = (8 + 2x) m

Area of the rectangular garden including surrounded uniform width = (10 + 2x) * (8 + 2x)

= 10(8 + 2x) + 2x(8 + 2x)

= 80 + 20x + 16x + 4x²

= (80 + 36x + 4x²) m²

So, Area of the rectangular garden including surrounded uniform width = (80 + 36x + 4x²) m²

Subtract area of rectangular garden from Area of the rectangular garden including surrounded uniform width.

Area of surrounded road = Area of the rectangular garden including surrounded uniform width - Area of the rectangular garden

80+36x+4^2-80

36x+4x^2

So, Area of surrounded road = (4x² + 36x) m²

Hope This will help you

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