A rectangular sandbox

Question

A rectangular sandbox is surrounded on all sides by a strip of grass that is

55

feet wide on all sides. The length of the sandbox is

44

feet more than the​ width, and the total area for the sandbox and the grass is

189189

square feet. Find the dimensions of the sandbox.

Answer 1

The length is w+4+5+5 = w+14

the width is w+5+5 = w+10

length * width = area

(w+14)(w+10) = 189

w^2 + 24w + 140 = 189 <-- FOIL

w^2 + 24w - 49 = 0 <--- solves

w = [ -24 +or- sqrt( 24^2 - 4*-49)]/2

= [ -24 +or- sqrt( 576 + 196)]/2

= [ -24 +or- sqrt( 772)]/2

= [ -24 +or- sqrt( 2*2*193)]/2

= [-24 +or- 2 * sqrt(193)]/2

= -12 +or- sqrt(193)

= sqrt(193) - 12

= 1.8924439894498045.......

the length is 5.8924439894498045 = sqrt(193) - 8