Question

A path of uniform width runsround the inside of a rectangularfield 38 m long and 32 m wide.If the path occupies 600sq.m, then the width of the path is

• A. 30 m
• B. 5 m
• C. 18.75 m
• D. 10 m

Answer 1

Answer:

B. 5 m

Let the width of path be x m.

Area of rectangular field = 38 × 32 = 1216 sq.m

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= 30

The Width of path be 5m