# The ratio of the two sides of the rectangle is 4: 9, and its perimeter is 52cm. Find the sides of the given rectangle.

March 25, 2021 | education

| In order to find the sides of a rectangle, we will compose and solve an equation. Let’s start by analyzing the problem statement.

From the condition it is known that the perimeter of the rectangle is 52 cm, and it is also known that the sides relate to each other as 4: 9.

We introduce the coefficient of similarity x, then the lengths of the sides can be written as 4x and 9x cm.

P = 2 (a + b);

We compose and solve the equation:

2 (4x + 9x) = 52;

x (4 + 9) = 52: 2;

13x = 26;

x = 26: 13;

x = 2.

Then

4 * 2 = 8 cm one of the sides, then 9 * 2 = 18 cm the length of the second side.

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