The perimeter of an isosceles triangle is 52 cm. The middle line connecting the midpoints of the sides is

The perimeter of an isosceles triangle is 52 cm. The middle line connecting the midpoints of the sides is 7 cm. Find the side of the triangle

1. Vertices of triangle A, B, C. KE – middle line.

2. We calculate the length of the base of the AC of a given triangle, taking into account that it is twice as large as KE:

AC = KE x 2 = 7 x 2 = 14 centimeters.

3. By the condition of the problem, the given triangle is isosceles. Therefore, the sides are equal. That is, AB = BC.

4. Calculate their length using the formula for calculating the perimeter (P) of a triangle:

P = AB + BC + AC.

AB = BC = (P – AC) / 2 = (52 – 14) / 2 = 19 centimeters.

Answer: each of the sides AB and BC is 19 centimeters.