A square and a rectangle have the same perimeter of 108 cm. The length of the rectangle is 6 cm greater than the average of all its sides. Which of the two figures has a greater area and by how many cm2?

Question

anonymous · Answer

Average of all sides of rectangle = (2L + 2W) / 4 = (L+W)/2

L = (L+W)/2 + 6
=> 2L - 12 = L + W

We also know L + W = 108/2
=> L + W = 54

So, 2L - 12 = 54
=> 2L = 66
=> L = 33
=> W = 21
Area = 33 * 21 = 693 sq cm

Area of square = 27*27 (since each side is 108/4) = 729 sq cm.

anonymous · Answer

Thanks so much!!!  This helped me a lot!!