You see a rectangle that has been made by putting seven congruent rectangles together. The perimeter of the large rectangle is 114 cm. What is its area?
Solution
The perimeter is 6x + 5y = 114.
4x = 3y (the length of the big rectangle)
x = 3y/4, so 6(3y/4) + 5y = 114
18y + 20y = 456, i.e. 38y = 456, so y = 12 and x = 9.
The area = 4x(y + x) = 36 x 21 = 756 sq. cm.
