An isosceles triangle ABC base AC is one cm smaller than its lateral side ABC perimeter equal to 23 cm find base AC.

In an isosceles triangle, the sides are equal. Let x cm be the length of the side.

Then (x – 1) cm is the length of the base of this triangle.

It is known that the perimeter of a triangle is equal to the sum of the lengths of all its sides, then (x + x + (x – 1)) cm is the perimeter △ ABC. According to the condition of the problem, it is 23 cm, which means that you can write the following expression:

x + x + (x – 1) = 23.

Let’s solve the equation:

x + x + x – 1 = 23,

3x – 1 = 23,

3x = 23 + 1,

3x = 24,

x = 24: 3,

x = 8.

8 cm – the length of the side △ ABC.

Calculate the base length:

8 – 1 = 7 cm.

Answer: 7 cm.