Question

perimeter of a triangle is 44 cm it side is in the ratio 9:7:6 find its area

Answer 1

Given : the side of the Triangles are 9 : 7 : 6 and its perimeter is 44 cm

To find : It's area

Solution: Let the common factor be x

⟹ 9x : 7x : 6x

We know that the perimeter of the triangle =sum of the side of the triangle

⟹ perimeter of the triangle = 44cm ( given )

Therefore

9x +7x + 6x = 44 cm

⟹ 22x = 44cm

$\implies \: x = \dfrac{ \cancel{44}}{ \cancel{22} }$

$\bold{ \implies \: x = 2 \: cm}$

Therefore,

The sides of the triangle are

$9x = 9 \times 2 = 18 \: cm\\ 7x = 7 \times 2 = 14 \: cm\\ 6x = 6 \times 2 = 12 \: cm$

Now,

The semi perimeter of the triangle = 44/2

= 22

By using Heron's formula

$\sf{ Area \: of \: triangle } = \sqrt{s(s - a)(s - b)(s - c)}$

$\implies \: \sqrt{22(22 - 18)(22 - 14)(22 - 12)}$

$\implies \: \sqrt{22(4)(8)(10)}$

$\implies \: \sqrt{7040}$

$\implies \: \large{ \bold { 83.904}}$ (approx)