- 460 sq. m
- 468 sq. m
- 288 sq. m
- 360 sq. m
- 424 sq. m
Option 1 : 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