Question

A rectangular field, 70 m long and 50 m wide, is surrounded by a concrete path of uniform width. Given that the area of the path is 1024 m, find the width of the path.

Answer 1

let width of path x m

Area of field + path

[ 70 + 2x ] [ 50 + 2x ] = 3500 + 240x + 4x² m²

area of path = 240x + 4x² m²

240x + 4x² = 1024

x² + 60x - 256 = 0

[ x + 64 ] [ x - 4 ] = 0

x = 4

Width of path = 4 m