In an isosceles triangle ABC with a base AC, the lateral side is 25 cm.The median BD = 15 cm

In an isosceles triangle ABC with a base AC, the lateral side is 25 cm.The median BD = 15 cm. Find the length of the median DE (E belongs to AB), if the perimeter of the triangle ABC = 60 cm, BD = 15 cm.

Given:
triangle ABC – isosceles (AB = BC)
AB = BC = 25 cm
BD – median of triangle ABC, BD = 15 cm
DE – median of triangle ABD
P (ABC) = 60cm
Find: DE -?
Decision:
Since ABC is an isosceles triangle, by the property of an isosceles triangle, BD is also height, which means that triangle ADB is right-angled. Hence, DE is the median of a right-angled triangle. By the property of the median drawn from the vertex of the right angle, it is equal to half of the hypotenuse, that is, AB / 2. This means DE = AB / 2 = 25/2 = 12.5 cm
Answer: 12.5 cm