A foothpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 sq. m, find the width of the foothpath.

Let the width of the rectangular path be x m.

Area of the rectangular field = 32 x 24 = 768 square metre.

Area of the path = 768 - (32 - 2x)(24 - 2x) = - 4x² + 112x = 208

Or, - x² + 28x = 52

Or, x² - 28x + 52 = 0

Therefore, x = 2 m