Question

A garden measuring 16 meters by 8 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 240 square meters. What will be the width of the pathway?

Answer 1

Answer:

2 m

Step-by-step explanation:

First we need to calculate the actual area of the garden:

Area = 16 * 8 = 128 m2

If the new area is 240 m2 and we call the width of the pathway 'w', we have that:

New area = (16+2w) * (8+2w) = 240

128 + 48w + 4w^2 = 240

4w^2 + 48w - 112 = 0

w^2 + 12w - 28 = 0

Delta = 12^2 + 4*28 = 256

sqrt(Delta) = 16

w1 = (-12-16)/2 = -14 m (not a valid width)

w2 = (-12+16)/2 = 2 m