Correct Answer - Option 2 : 5 m
Given:
A path of uniform width runs round inside the rectangular field of 38 m long and 32 m wide. if the path occupies 600 m2.
Concept used:
Area of rectangle = Length × Breadth
Calculation:
Let the width of path be x m.
Area of rectangular field = 38 × 32 = 1216 m2
Area of rectangular field without path = (38 - 2x) (32 - 2x)
⇒ 1216 - 64x - 76x + 4x2
⇒ 4x2 - 140x + 1216
Area of path
⇒ 1216 - (4x2 - 140x + 1216)
⇒ 140x - 4x2
The path of the rectangular field occupies is 600 m2
⇒ 140x - 4x2 = 600
⇒ 4x2 - 140x + 600
⇒ x2 - 35x + 150
⇒ x2 - 30x - 5x + 150
⇒ x(x - 30) - 5(x - 30)
⇒ (x - 5) (x - 30)
∴ x = 5 because \(x \ne 30\)
∴ x = 5m is the width of the path.