Question

A footpath of uniform width runs all around the outside of a rectangular field 30 m long and 24 m wide. If the path occupies an area of 360 m², find its width.

Answer 1

Let x be the width of the footpath.
Then
Area of footpath = `2 xx ( 30 + 24 )x + 4x^2`
                            = 4x² + 108x

Again it is given that the area of the footpath is 360sq.m.
Hence,
4x² + 108x = 360
x² + 27x - 90 = 0
( x - 3 )( x + 30 ) = 0
x = 3
Hence width of the footpath is 3m.