# In the triangle ABC, BM is the median and BH is the height. It is known that AC = 56 and BC = BM. Find HA.

December 29, 2020 | education

| Consider the triangle MBC. If BC = BM is an isosceles triangle, and the height of BH in an isosceles triangle is the median, then MH = HC.

From the condition BM – median, then AM = MC.

MC = MH + HC.

Start up HC – x.

Let’s compose and solve the equation.

AC = AM + MH + HC = 2x + x + x;

56 = 4x;

x = 56: 4;

x = 14.

We define AH.

AH = AM + MH = 2x + x = 3x = 3 * 14 = 48.

Answer: AH = 48.

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