Given a triangle with sides 13,14,15 cm. Find its height drawn to the largest side.

1. Vertices of the triangle – A, B, C. The lengths of the sides AB, BC, AC are respectively 13, 14, 15 centimeters. BH is the height drawn to the AC side (greatest).

2. Calculate the area (S) ΔABC using Heron’s theorem:

S = √p (p – AB) (p B) (p – AB).

In this formula, p is the semiperimeter ΔABC.

p = (AB + BC + AC) / 2 = (13 + 14 + 15) / 2 = 21 centimeters.

S = √21 (21 – 13) (21 – 14) (21 – 15) = √21 x 8 x 7 x 6 = √7056 = 84 centimeters².

3. We calculate the length of the HH height using another formula for calculating the area ΔABC:

S = AC x BH / 2.

BH = 2 x S / AC = 2 x 84/15 = 11.2 centimeters.

Answer: The length of the HV height is 11.2 centimeters.