The side of an isosceles triangle is 10cm, and the perimeter is 26cm, what is the base length?

An isosceles triangle is given.
Let’s call this triangle ABC.
By condition, the side of this triangle ABC is 10 cm.
Also, by condition, the perimeter of ABC is 26 cm.
Find the length of the base of triangle ABC, that is, the length AC.
Since triangle ABC is isosceles by assumption, its sides are equal. Hence, we can write that AB = BC.
Now let’s write down the formula by which the perimeter of the triangle ABC is calculated.
P = AB + BC + AC.
Since AB = BC, this perimeter formula can be written in a different way.
P = 2AB + AC.
Next, we will express how to find the base length AC.
AC = P – 2AB.
Now we substitute the values ​​of P and AB known by the problem statement.
AC = 26 – 2 × 10.
AC = 26 – 20.
AC = 6 (cm).
Answer: 6 cm is the length of the base.