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

In an isosceles triangle, the height drawn to the base is the median, that is, it divides the base into two equal segments.

Triangles ABD and DBC are equal (on three sides AB = BC, AD = DC, BD is common), angle D is straight (BD is height).

By the Pythagorean theorem:

AB ^ 2 = AD ^ 2 + BD ^ 2;

BD ^ 2 = AB ^ 2 – AD ^ 2;

BD = √ (AB ^ 2 – AD ^ 2).

AB = 37; AD = AC: 2 = 24: 2 = 12.

BD = √ (37 ^ 2 – 12 ^ 2).

Under the square root sign, we factor the difference of the squares:

BD = √ (37 – 12) (37 + 12);

BD = √ 25 × 49;

BD = 5 × 7;

BD = 35 cm.