Find the dimensions of the sandbox.

Question

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

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

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

189 square feet. Find the dimensions of the sandbox.

Answer 1

L = 2+w

189 = (L+5)(w+5) = (2+w+5)(w+5) = (w+7)(w+5) = w^2 +12w + 35

w^2 +12w - 174 = 0

factor try

(w + 29)(w-6)= 0 but not possible

complete the square

w^2 +14w+49=189+49

(w+7)^2= 238

w+7= +/-sqr238

w=-7+/- sqr238= about

22.4272, 8.4272

about 22.4 ft by 8.4 ft