Find the area of the rectangle if the perimeter of the rectangle is 56 cm, and one side is 3 times smaller than the other.

1) Let’s introduce a variable.

x cm – the length of the smaller side of the rectangle;

3x cm – the length of the larger side of the rectangle.

2) Let’s make an equation.

The perimeter of a rectangle is equal to the sum of the lengths of its four sides. P = 2 (a + b).

For our case, the perimeter of the rectangle is 2 (x + 3x) cm or 56 cm.We get the equation 2 (x + 3x) = 56.

3) Having solved the equation, we find the sides of the rectangle.

2 * 4x = 56;

8x = 56;

x = 56: 8;

x = 7 (cm) – the length of the smaller side;

3x = 7 * 3 = 21 (cm) – the length of the longer side.

4) Find the area of ​​the rectangle.

The area of ​​a rectangle is equal to the product of its sides. S = av.

7 * 21 = 147 (cm²).

Answer. 147 cm².