A developer wants to build homes on a rectangular plot of land 4 kilometers long and 3 kilometers wide. In this part of the city, regulations require a greenbelt of uniform width along two adjacent sides. The greenbelt must be 10 times the area of the development. find the width of the greenbelt.

Answer 1

area of development = 3*4 = 12 km^2
greenbelt area = 120 km^2:
one end = (3+w) by w
other end = 4 by w
so
120 = 4 w + 3 w + w^2 = w^2 + 7 w

w^2 + 7 w - 120 = 0

w = [ -7 +/- sqrt (49+480) ] / 2
= [ -7 +/- 23]/2
use + root only
w = 8