Question

A path of uniform width runs round the inside of a rectangular field 38 m long and 32 m wide. If the path occupies 600m² , then the width of the path is

• A. 30m
• B. 5m
• C. 18.75m
• D. 10m

Answer 1

Answer:

B. 5m

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

= 1216 – 140x + 4x²

Area of the path = 1216 – 1216 + 140x – 4x²

= 140x – 4x²

140x – 4x² = 600

4x² - 140x + 600 = 0

x² – 35x + 150 = 0

x² – 30x –5x +150 = 0

x (x– 30) –5 (x –30) = 0

(x– 5) (x –30) = 0

$x = 5 as x^1=30$

Hence Width = 5m