# The perimeter of the ABC triangle is 38 cm, the AB side = 13 cm. The BC side is 5 cm

**The perimeter of the ABC triangle is 38 cm, the AB side = 13 cm. The BC side is 5 cm larger than the AC side. Calculate the lengths of the unknown sides of a given triangle.**

Given:

triangle ABC,

the ABC perimeter is 38 centimeters,

AB = 13 centimeters,

BC – AC = 5 centimeters.

Find the lengths of the sides of the triangle BC and AC -?

Solution:

Consider a triangle ABC.

The perimeter of a triangle is the sum of the lengths of all its sides.

Let us express the side of the sun:

BC = AC + 5.

Then the perimeter of the triangle ABC will be equal to:

AB + BC + AC = 38;

Since AB = 13 centimeters, and BC = AC + 5, then

13 + AC + 5 + AC = 38;

2 * AC + 18 = 38;

2 * AC = 38 – 18;

2 * AC = 20;

AC = 10 centimeters;

BC = 10 + 5;

BC = 15 centimeters.

Answer: 10 centimeters; 15 centimeters.