Question

The sides of a triangle are 35 cm, 54cm and 61cm respectively, then the length of its
longest altitude is ____

Answer 1

In a triangle the shortest side acts as the base for the longest altitude.

Here, in the given question the side of 35 cm length is the shortest. Hence it will act as the base for the longest altitude.

Thee altitude divides its base into two parts.

Let's assume the length of one part be x. Then the length of the second part will become (35 - x).

Now by using Pythagoras theorem the length of the altitude is given by.

L²= [54²-x²]........(i) and also by

L²= [61²-(35-x)²]........(ii)

By substracting eq(i) from eq (ii) we get

61²-54²-(35-x)²+x²=0

70x =420

x=6

Now substituting the value of x in eq (i) we get

L² =54²-6²

L=√2880

L =24√5