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A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn which has an area of 420 sq. m. If the width of the path is 4 m and the length of the plot is greater than its breadth by 36 m, what is the area of the rectangular plot? 

A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn which has an area of 420 sq. m. If the width of the path is 4 m and the length of the plot is greater than its breadth by 36 m, what is the area of the rectangular plot?  Correct Answer 460 sq. m

Area of rectangle = Length × Breadth

Let,

Breadth of the plot = x m

Length of the plot = (x + 36) m

∴ Area of the plot = x(x + 36) sq. m

Given,

Width of the path = 4 m

∵ Path is running parallel to the breadth

∴ Length of the path = x m

Area of the path = 4x m

∴ Area of the rest of plot = Area of the plot - Area of the path

⇒ 420 = x(x + 36) - 4x

⇒ 420 = x2 + 32x

⇒ x2 + 32x - 420 = 0

⇒ x2 + 42x - 10x - 420 = 0

⇒ x(x + 42) - 10(x + 42) = 0

⇒ (x + 42)(x - 10) = 0

⇒ x = 10 (∵ x ≠ -42 )

∴ Area of the plot

= 10(10 + 36) sq. m

= (10 × 46) sq. m

= 460 sq. m

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