In triangle ABC, side BC is twice as large as side AB and 7 cm shorter than side AC.

In triangle ABC, side BC is twice as large as side AB and 7 cm shorter than side AC. Find all sides of the triangle if its perimeter is 52 cm.

Let us denote by the variable k the number of centimeters to which the side AB is equal.

Accordingly, the value of the length of the AC side of this triangle we can represent in the form 2k, and the value of the length of the AC side of this triangle we can represent in the form (2k + 7).

Since we know that the value of the perimeter of a geometric figure is 52 centimeters, we write down the equation and find its sides:

k + 2k + 2k + 7 = 52;

5k = 45;

k = 9;

2 * 9 = 18;

18 + 7 = 25.

Answer: Side AB 9 cm, BC – 18, AC – 25.