Expert: Lynn Houston - 7/7/2009

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

Answer
63cm

the rectangle is 1000x1500cm for a total of 1,500,000cm^2.  20% of 1,500,000cm is 300,000, so the boardwalk has to = 300,000cm^2

Let x = the width of the boardwalk, therefore

1500x + 1500x + 1000x +1000x - 4x^2 = 300000 (4x^2 is the overlap in the corners)

4x^2-5000x + 300000 = 0.  Use the quadratic eq

(-b +- sq rt (b^2-4ac))/2a  and you get x = 63.193874 or 63cm