Question

The length 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:

area of triangle = √s(s-a)(s-b)(s-c)

Side = a+b+c

2

66 cm = Side

Area √66(66-33) (66-44) (66-55)

√66×33×22×11

2×3×11×3×11×2×11×11 ( Factors of 66×33×22×11)

726 cm²

Height =

Area of right triangle=

$\frac{1}{2} \times product \: of \: its \: leg$

726cm² =

$\frac{1}{2} \times 44 \times height$

= 2×726

44

Hence, height is 33 cm