Maths problem Concerning Inequalities

Question

A 38m rope is used to form a rectangular area on a sports day. If the width of the rectangle has to be at least 2 m long, and the length has to be exactly 1 m longer than its width, find the maximum dimensions of the rectangle. 

Answer 1

Let w be the width of the rectangle. Ten, the length is w + 1 since it is exactly 1 m longer than the width.

 

Since the rope is 38 m long, this would be the perimeter. 

 

Now, p = 2 (l+w) or 38 = 2(w+1+w) = 2(2w+1).

 

If 38 = 2(2w+1), then 19 = 2w + 1 and 18 = 2w so w = 9 and w + 1 = 10

 

So, this rectangle measures 9 m by 10 m and has an area of 90 square meters.