Question

The perimeter of a
triangle
is 44cm. it's sides are in ratio 9:7:6. find its area​

Answer 1

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

To find : Its area

Solution: Let the ratio is x

⟹ 9x : 7x : 6x

We know that ,

the perimeter of a triangle =sum of the three side of the triangle

⟹ perimeter of the triangle = 44cm

Therefore,

9x +7x + 6x = 44 cm

⟹ 22x = 44cm

=> x = 44/22

=> x = 2 cm

Hence,

the side of triangle are,

9x = 9 ×2 = 18cm

7x = 7× 2 = 14cm

6x = 6 × 2 = 12cm

Now,

calculate the semi perimeter of the triangle :- 44/2

= 22cm

$area \: \: of \: \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \: \: \: \: \: = \sqrt{22(22 - 18)(22 - 14)(22 - 12)} \\ = \sqrt{22(4)(8)(10)} \\ = \sqrt{7040}$

= 84 cm² approx

Answer 2

Question ⤵️

The perimeter of a triangle is 44cm. it's sides are in ratio 9:7:6. find its area?

Answer ⤵️

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

To find : Its area

Solution: Let the ratio is x

⟹ 9x : 7x : 6x

We know that ,

the perimeter of a triangle =sum of the three side of the triangle

⟹ perimeter of the triangle = 44cm

Therefore,

9x +7x + 6x = 44 cm

⟹ 22x = 44cm

=> x = 44/22

=> x = 2 cm

Hence,

the side of triangle are,

9x = 9 ×2 = 18cm

7x = 7× 2 = 14cm

6x = 6 × 2 = 12cm

Now,

calculate the semi perimeter of the triangle :- 44/2

= 22cm

$\begin{gathered}area \: \: of \: \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \: \: \: \: \: = \sqrt{22(22 - 18)(22 - 14)(22 - 12)} \\ = \sqrt{22(4)(8)(10)} \\ = \sqrt{7040} \end{gathered}areaoftriangle=s(s−a)(s−b)(s−c)=22(22−18)(22−14)(22−12)=22(4)(8)(10)=7040$

= 84 cm² approx