November/December 2013 Maths Challenge

Seamus is using all 120 inches of a piece of copper wire to build a rectangle that is five times as long as it is wide, and a square whose side length is the same as the width of the rectangle.

What will be the exact area of the square?

Suggested Solution:
Let w represent the width of the rectangle. Then 5w is the length of the rectangle, and w is the side length of the square. The perimeter of the rectangle
is 5w + w + 5w + w = 12w,
and the perimeter of the square is
w + w + w + w = 4w.
Therefore, the total of the lengths of all four sides of the rectangle and all four sides of the square is
12w + 4w = 16w.
16w = 120 in.,
w = 120/16 = 7.5 in.
The area of a square with side length w = 7.5 in. is
(7.5 X 7.5)  

= 56.25  square inches

** The winner of the November/December Maths Challenge was Gelaine Elises of Lucan Community College. Gelaine was named Mathematician of the Month and won a gift voucher worth EUR100. **