Find the height of the triangle to the larger side of the triangle if the sides of the triangle are 13 cm, 37 cm, and 40 cm.

1. Vertices of the triangle – A, B, C. AB = 13 cm. BC = 37 cm AC = 40 cm. S – area

triangle. ВН – height. P is half the perimeter.

2. The area of the triangle is calculated by the formula of Heron’s theorem:

S = √P (P – AB) (P – BC) (P – AC).

P = (AB + BC + AC) / 2 = (13 + 37 + 40) / 2 = 45 cm.

S = √45 x 32 x 8 x 5 = √57600 = 240 cm².

3. We calculate the length of the ВН height using another formula for calculating the area of a triangle:

S = AC / 2 x HВ.

BH = S: AC / 2 = 240: 20 = 12 cm.

Answer: The length of the HВ height is 12 cm.