Question

A field measuring 12 meters by 16 meters is to have a brick paver walkway installed all around it, increasing the total area to 285 square meters. How wide will the walkway be? (1.5 m)

Answer 1

1.5 m

Step-by-step explanation:

Length. L = 12 m

Width, W = 16 m

Area, A = 12 x 16 = 192 m^2

Let the width of pavement be d.

The new length, L' = 12 + 2d

the new width, W' = 16 + 2d

New Area, A' = L' x W' = (12 + 2d)(16 + 2d) = 192 + 56 d + 4d^2

Difference in area = A' - A

285 = 192 + 56 d + 4d^2 - 192

93 = 56 d + 4d^2

4d^2 + 56 d - 93 = 0

`d = \frac{-56\pm \sqrt{56^(2)+4* 4* 93}}{8}`

`d=(-56\pm 87.72)/(8)`\

d = 1.5 m

Thus, the width of the pavement is 1.5 m.