Question

a uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15 m. if the boardwalk takes up 20% of the lot, how wide is the boardwalk to the nearest centimetre?

Answer 1

Start by finding the area. 15*10 = 150m^2.

20% of 150 is 30m^2. That is the area of the boardwalk.

Now, if you draw a picture, you will realize that finding the width is more complex than multiplying by the perimeter. The boardwalk is on the inside edge, so the perimeter is shortened according to the width.

Allowing the 15m side to remain at full length, the area the boardwalk takes up comes out to 2*(15*x+(10-x)*x)

Therefore, 2*(15x+10x-x^2) = 30
50x - 2x^2 = 30
x^2 - 25x + 15 = 0

Use the quadratic equation to solve for x:
x = (25 +/- sqrt(25^2 - 4*15*1))/2
x = 25 +/- sqrt(625-60))/2

x = 0.615m, 24.385m.

The latter is not possible because the boardwalk is 10m by 15m. Therefore, x = 0.615m.

In centimeters, that is 0.615*100, 0r 61.5cm. To the nearest centimeter, that would be 62cm.