# The sides of a triangle are 2: 3: 4, and its perimeter is 22.5 cm. Find the length of the smallest side of this triangle.

June 30, 2021 | education

| 1. Vertices of the triangle A, B, C. P is the perimeter.

2.AB: BC: AC = 2: 3: 4.1.

We take for x the number of units of length (centimeters) per part:

3. P = AB + BC + AC = 22.5.

4. Let’s make the equation:

2x + 3x + 4x = 22.5.

9x = 22.5.

x = 2.5 centimeters.

AB = 2 x 2.5 = 5 centimeters.

BC = 3 x 2.5 = 7.5 centimeters.

AC = 4 x 2.5 = 10 centimeters.

The smaller side AB = 5 centimeters.

Answer: AB = 5 centimeters – the smaller of the sides of the triangle.

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