The sides of a triangle are 35 cm, 54 cm, and 61 cm respectively. Find the length of its longest altitude.
(i) First, determine the semi-perimeter, s and then determine the area of the triangle by using Heron’s formula.
(ii) For the longest altitude, take base as the smallest side. Apply the formula,
(iii) Equate the area obtained using the two formulae and obtain the required height.
Let ABC be a triangle in which sides AB = 35 cm, BC = 54 cm, CA = 61 cm
Now, semi-perimeter of the triangle,
[∵ semi−perimeter, s=a+b+c2]
∵ Area of ΔABC=√
Also Area of ΔABC=12×AB×Altitude
Hence, the length of altitude is 24√ cm