Question

the lengths of the sides of a triangle are 33cm, 44cm, and 55cm respectively. find the area of the triangle and hence find the height corresponding to the side measuring 44cm.​

Answer 1

semiperimeter = (33 + 44 + 55)/2

= 66 cm

use hero's formula ,

area of triangle =root {66 (66- 33)(66-44)(66-55)}

=root {66 x 33 x 22 x 11 }

=11 x 11 x 6 = 121 x 6 = 726 cm^2

area of triangle = 1/2 height x base

726 = 1/2 height x 44

height = 726/22 =33 cm

Answer 2

Step-by-step explanation:

Lengths of the triangle = 33 cm , 44 cm , 55 cm

Close observation on values:

33 : 44 : 55 = 3 : 4 : 5        ['11' common in all the terms]

This ratio is of 'a right angled triangle'.

Area = 1/2 * b * h = 1/2 * 33 * 44 = 726 cm²

case 2: Height of side measuring 44 cm

A = 1/2 * b*h

726 = 1/2 * 44 * h

h = 726*2/44 = 33 cm