Question

a triangle has sides 35 cm, 54cm,61cm long. find it's smallest altitudes​

Answer 1

Given:

• The sides of triangle are 35cm , 54cm and 61cm.

To Find:

• The smallest altitude = ?

Solution:

Let x = 35cm , y = 54cm and z= 61cm.

Now,

perimeter a + b + c = 25 

⇒ S = 1/2 (35 + 54 + 61) 

⇒ s = 75 cm

By using heron's formula:

Area of triangle = √s(s-a)(s-b)(s-c)

= √75(75-35)(75-54)(75-61)

= √75(40)(21)(14)

= 939.14cm

The altitude will be a smallest when the side corresponding to it is longest Here, longest side is 61 cm.

$\therefore \: \sf \: area \: of \triangle = \frac{1}{2} \times base \times height \\ = \sf \: \frac{1}{2} \times h \times 61 = 939.14cm \\ \sf \: \implies \: h = \frac{939.14 \times 2}{61} \\ \sf \height \: = 30.79cm$

Hence the length of the smallest altitude is 30.79 m.