The lateral side of an isosceles triangle is 10 cm, and its perimeter is more than 37 cm. How long can the base

The lateral side of an isosceles triangle is 10 cm, and its perimeter is more than 37 cm. How long can the base of a triangle have if it is known that this length (in cm) is expressed by a natural number?

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

Since we have an isosceles triangle, both sides are 10 cm.

Let’s say a third party – b see.

The perimeter is:

P = 10 + 10 + b = (20 + b) cm.

According to the terms of the assignment, the perimeter is more than 37 cm. Means:

20 + b ˃ 37;

b ˃ 17.

But on the other hand, the side of the triangle cannot be more than the sum of the other two sides (in our case, 20). I.e:

20 ˃ b ˃ 17.

This means that the base of the triangle can be either 18 cm or 19 cm.

Answer: 18 cm or 19 cm.