In an isosceles triangle, the lengths of two sides are known: 13m and 24m. What can be the perimeter of this triangle.

Let us denote by a, b and c – the sides of the triangle. The condition for the existence of a triangle is that the sum of any two sides of a triangle must be greater than the third. That is, (a + b)> c, (a + c)> b, (b + c)> a.

Moreover, the triangle is isosceles, therefore, the sides at its base are equal.

Substitute the numerical values.

Let a be the base of the triangle = 13 (m), then b and c are sides at the base = 24 (m), then: (13 (m) + 24 (m))> 24 (m) or 37 (m)> 24 (m); (13 (m) + 24 (m))> 24 (m) or 37 (m)> 24 (m); (24 (m) + 24 (m))> 13 (m) or 48 (m)> 13 (m). All conditions are met, therefore, a triangle with a base of 13 meters and sides of 24 meters exists, while its perimeter will be: P = a + b + c = 13 (m) + 24 (m) + 24 (m) = 61 ( m).

Let a be the base of the triangle = 24 (m), then b and c are the sides at the base = 13 (m), then: (24 (m) + 24 (m))> 13 (m) or 48 (m)> 13 (m); (24 (m) + 13 (m))> 13 (m) or 37 (m)> 13 (m); (13 (m) + 13 (m))> 24 (m) or 26 (m)> 24 (m). All conditions are met, therefore, a triangle with a base of 24 meters and sides of 13 meters also exists, while its perimeter will be: P = a + b + c = 24 (m) + 13 (m) + 13 (m) = 50 (m).

Answer: The perimeter of a triangle can be 61 meters and 50 meters.