# An example of a triangle ABC is 60 cm. The AB side is 5 cm larger than the AC side and the BC

An example of a triangle ABC is 60 cm. The AB side is 5 cm larger than the AC side and the BC side is 5 cm larger than the AB side. Find the sides of the triangle?

The perimeter of triangle ABC is

P = AB + BC + AC.

It is known that

AB = AC + 5,

but

BC = AB + 5.

From here

BC = (AC + 5) + 5 = AC + 10.

Now that we have all the parties expressed through the AC side, we can write an equation and solve it. Let’s do it:

(AC + 5) + (AC + 10) + AC = 60,

AC + 5 + AC + 10 + AC = 60,

3AC + 15 = 60,

3AC = 45,

AC = 45/3,

AC = 15 cm.

Find side AB:

AB = 15 + 5 = 20 cm.

Now let’s find the BC side:

BC = 15 + 10 = 25 cm.

Answer: the sides of triangle ABC are equal: AB = 20 cm, BC = 25 cm, AC = 15 cm.

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