Problema Solution
Caroline is trying to build a pig pen. The pen is 14 feet long and 6 feet wide. Around the entire pen is a walkway. It is twice as wide along the lengths as it is along the widths. If the area of the walkway is 120 square feet, how wide is the walkway along the length?
Answer provided by our tutors
let
l = 14 ft the length of the pen
w = 6 ft the width of the pen
x = the width of the walkway along the widths, x>0
2x = the width of the walkway along the lengths
A = 120 ft^2 is the area of the walkway
the length of the pen together with the walkway is: l + 2*2x
the width of the pen together with the walkway is: w + 2x
the area of the pen and the walkways is: (l + 2*2x)*(w + 2x)
the area of the pen is: l*w
A is the difference between the two areas above that is
A = (l + 2*2x)*(w + 2x) - lw
(14 + 4x)(6 + 2x) - 14*6 = 120
by solving the quadratic equation and considering only the non-negative and real roots we find
x = 1.80594 ft = 1.8 ft to the nearest tenth
2x = 3.61908 ft = 3.6 ft to the nearest tenth
the width of the walkway along the length is 3.6 ft.