# In an isosceles triangle ABC AB = BC = 37 cm, AC = 24 cm. Find the length of the height BD.

May 26, 2021 | education

| Since in an isosceles triangle, the height drawn from the vertex between the lateral sides is both the bisector and the median, it will divide it into 2 equal parts.

Let’s calculate the length of one of the halves of the base AC:

AD = DC = 24/2 = 12 cm.

Through the Pythagorean theorem, we express the unknown leg, which in this case is the height, and find its value:

BD = √ (37 ^ 2 – 12 ^ 2) = √ (1369 – 144) = √ (1225) = 35 cm – the length of the height of an isosceles triangle.

Answer: 35 cm.

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