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

December 30, 2020 | education

| **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

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