Problema Solution
A garden measuring 12 meters by 21 meters is to have a pedestrian pathway installed all around it, increasing the total area to 468.16 square meters. What will be the width of the pathway?
Answer provided by our tutors
let
x = width of the pathway
the area of the rectangle = width * length
then the total area = to the area of the rectangle with width and length (12 + 2x) and (21 + 2x) that is
(12 + 2x)*(21 + 2x) = 468.16
4x^2 + 66x + 338 = 468.16
by solving the quadratic equation we find 2 solution
x1 = 2.8
x2 = -19.3
since the width of the pathway can only be positive number the answer is 2.8 m:
the width of the pathway will be 2.8 m.