The square and rectangle have a common side (width for the rectangle). The width and length of the rectangle are 1: 3.

The square and rectangle have a common side (width for the rectangle). The width and length of the rectangle are 1: 3. The side of the square is 42 cm less than the perimeter of the rectangle. Find the area of a square.

Let the width of the rectangle be x, then its length is 3x, and the perimeter of the rectangle is x + x + 3x + 3x = 8x.
The side of the square is equal to the width of the rectangle, on the other side it is 42 cm less than the perimeter of the rectangle. We can make an equation:
x = 8x-42;
7x = 42;
x = 42/7 = 6 cm – the width of the rectangle and the side of the square.
The area of a square is equal to the square of its side: S = 6 ^ 2 = 36 cm2.