Finding what the length and width of the runway in meters

Question

To accommodate the largest jets, an international airport runway is 1500 m more than 50 times its width. If the perimeter of the runway is 11,160 m, determine the length and width of the runway (in meters).

Answer 1

Perimeter of a rectangle:

P = 2L + 2W

It is given that L is 1500 m more than 50 times the width

So L = 1500 + 50W

And we know P = 11160, so substitute to get one equation with one unknown (W).

11160 = 2(1500 + 50W) + 2W

At this point we could divide every term by 2, but let's just distribute and simplify the right side.

11160 = 3000 + 100W + 2W

8160 = 102W

W = 8160/102 = 80m

L = 1500 + 50(80) = 1500 + 4000 = 5500m