3405.11 – Seven Rectangles

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).

$x = \dfrac{3y}{4}$ , so $6\left(\dfrac{3y}{4}\right) + 5y = 114$ . $18y + 20y = 456$ , i.e. $38y = 456$ , so $y = 12$ and $x = 9$ .

The area $= 4x(y + x) = 36 x 21 = 756 \cm^2$ .