Problema Solution
A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 286 square meters. What will be the width of pathway ?
Answer provided by our tutors
lets assume that the garden has rectangular shape
x = the width of the pathway and x>0
w = 12 m width of the garden
l = 16 m length of the garden
thus the dimensions of the garden together with the pathway will be
w + 2x = 12 + 2x
l + 2x = 16 + 2x
since the area of a rectangle = width * length
(12 + 2x)*(16 + 2x) = 286
4x^2 + 56x + 192 = 286
4x^2 + 56x - 94 = 0
by solving the quadratic equation we find the roots
x1 = 1.51 approximately
x2 = - 15.51
since the width is positive number the solution to our problem will be
x = 1.51 meters
the width of the pathway will be 1.51 meters.