A corner lot has dimensions 25 by 40 yards The city plans to

A corner lot has dimensions 25 by 40 yards. The city plans to take a strip of uniform width along the two sides bordering the streets to widen these roads. How wide should the strip be if the remainder of the lot is to have an area of 844 square yards?

Solution

area of corner lot = 25*40 = 1000 sq yards

let width of strip be w

area of first strip = 40w

area of 2nd strip = (25-w)w = 25w - w^2

total area of both strips = 40w + 25w - w^2 = 65w - w^2

area of remainder = 844 sq yards

therefore total area of strip 1000 - 844 = 156 sq yards

so we can write

65w - w^2 = 156

or   w^2 - 65w + 156 = 0

solving the quadratic equation we get

w = 2.5

so the strip must be 2.5 yards wide