The perimeter of one square is 3 times smaller than the perimeter of the second square.

| April 10, 2021 | education

The perimeter of one square is 3 times smaller than the perimeter of the second square. Find the area of the larger square if the sum of the perimeters of these two squares is 48 cm.

1) Let the perimeter of the first (smaller) square x (x) cm, then the perimeter of the second square: (x 3) cm.Knowing the sum of the perimeters of these two squares, we compose the equation:

x + x 3 = 48;

x 4 = 48;

x = 48: 4;

x = 12 (cm) – the perimeter of the smaller square.

2) Determine the perimeter of the larger square: x 3 = 12 3 = 36 or 48 – 12 = 36 (cm).

3) Find out the size of the side of the larger square: a = P: 4 = 36: 4 = 9 (cm).

4) Calculate the area of the larger square using the formula: S = a² = 9² = 81 (cm²).

Answer: the area of the larger square is 81 cm².



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