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

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.