Write down the expression for the perimeter of a triangle ABC if AB = a cm, AC is 2 times more, and BC is 15 cm more than AB.

Write down the expression for the perimeter of a triangle ABC if AB = a cm, AC is 2 times more, and BC is 15 cm more than AB. Make an equation and find the sides of triangle ABC, knowing that its perimeter is 95cm.

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

The length of the AC side is 2 times the length of the AB side, which means the length of the AB side multiplied by 2:

AC = 2 * AB = 2a (cm);

Side BC is 15 cm larger than side AB, which means add 15 cm to the length of side AB:

BC = (a + 15) cm;

Perimeter of triangle ABC:

P = a + 2a + (a + 15) = 95;

Let’s open the brackets and show similar ones:

4a + 15 = 95;

To find the unknown term, you need to subtract the known term from the sum:

4a = 95 – 15;

4a = 80;

To find an unknown factor, you need to divide the product by a known factor:

a = 80: 4;

a = 20 (cm) – side AB.

AC = 2a = 2 * 20 = 40 (cm);

BC = (a + 15) = 20 + 15 = 35 (cm).

Answer: the sides of the triangle are 20, 40 and 35 cm.