A rectangle has an area of 24cm. If it's length and width are whole numbers, what is the greatest possible perimeter?

Answer 1

If the area is 24cm² and one of the dimensions is represented by x the other dimension must be 24/x.

Since the sides of the rectangle must be whole numbers there are a limited number of possibilities for x and 24/x.

1 x 24

2 x 12

3 x 8

4 x 6

6 x 4

...

Now they start repeating. Calculate the perimeter for each possibility to determine the maximum possible perimeter. For example the 3 x 8 rectangle has a perimeter of 22 cm. The 2 x 12 has P = 28cm. You can take it from there!