Find the largest side of a rectangle if its perimeter is 136cm, and one side is three times the other.

1) Let’s designate the smaller of the sides of the rectangle as 1 part, then the larger side of the rectangle, according to the condition, is equal to 3 parts. The sum of the lengths of the sides of the rectangle is 1 part + 3 parts = 4 parts.

2) The perimeter of the rectangle is P = 2 (a + b), then the sum of the lengths of the sides of the rectangle is equal to a + b = P / 2, which means:

a + a = 136/2 = 136: 2 = 68 (cm)

3) According to 1) the sum of the lengths of the sides of the rectangle is 4 parts, and according to 2, the same sum is 68 cm.Let’s find what is 1 part:

68: 4 = 17 (cm) – 1 piece or the smaller side of the rectangle.

4) Find the large side of the rectangle:

17 * 3 = 51 (cm).

Answer: The largest side of the rectangle is 51 cm.