Question

The rectangular park has a joggers path of uniform width around it on the outside. If the area of the path is 258m2 and the dimensions of the park are 21m and 16m. Find the dimensions

Answer 1

Answer:

Let the width of the path be x m

So, AB = EF + 2x = (21 + 2x) m

BC = GF + 2x = (16 + 2x) m

Area of path = area of rect.(ABCD) – area of rect.EFGH

258 = (21 + 2x)(16 + 2x) – 21 × 16

258 = 4x2 + 32x + 42x

4x2 + 74x – 258 = 0

2x2 + 37x – 129 = 0

2x2 – 6x + 43x – 129 = 0

2x(x – 3) + 43(x – 3) = 0

So, x = 3 m

So, width of the path = 3 m.