# One side of the rectangle is 11 times smaller than the other. Find the sides of a rectangle if its perimeter is 144 cm.

June 26, 2021 | education

| Let us denote by x the smaller side of this rectangle, and by y – the larger side of this rectangle.

According to the condition of the problem, one of the sides of a given rectangle is 11 times smaller than the other, therefore, the following relation holds:

y = 11 * x.

It is also known that the perimeter of this rectangle is 144 cm, therefore, the following relationship holds:

2 * (x + y) = 144.

We solve the resulting system of equations. Substituting into the second equation the value y = 11 * x from the first equation, we get:

2 * (x + 11 * x) = 144.

We solve the resulting equation:

2 * 12 * x = 144;

24 * x = 144;

x = 144/24;

x = 6.

Knowing x, we find y:

y = 11 * x = 11 * 6 = 66.

Answer: the sides of this rectangle are 6 cm and 66 cm.

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