Question

A footpath of uniform width runs round the
inside of a rectangular field 32 m long and
24 m wide. If the path occupies 208 m², find
the width of the footpath.​

Answer 1

Answer:

$area \: of \: the \: path =area \: of \: larger \: reactangle - area \: of \: smaller \: rectangle \\ 208 = (32 + 2x) \times( 24 + 2x) - (32 \times 24) \\ 208 = 32 \times 24 + 64x + 48x + 4 {x}^{2} - 32 \times 24 \\ 208 = 112x + 4 {x}^{2} \\ 4 \times 52 = 4(28x + {x}^{2} ) \\ 52 = 28x + {x}^{2} \\ {x}^{2} + 28x - 52 = 0$