Question

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

Answer 1

HEY MATE!

HERE IS YOUR ANSWER.

>>>>>》 Given :- Perimeter of a Triangle = 44cm

It's sides = 9:7:6

Let the sides be 9x , 7x and 6x.

Therefore, Perimeter = a + b + c

9x + 7x + 6x = 44cm

22x = 44 cm

x = 44
-----
22

x = 2

Therefore , 9x = 9 × 2 = 18cm

7x = 7 × 2 = 14cm

and , 6x = 6 × 2 = 12 cm


Now ,

Let's find area of the given triangle.

S = a+b+c
----------
2

S = 18+14+12
-------------
2

S = 44
----
2

S = 22cm

Area of Triangle,

By Heron's Formula,

$\sqrt{s(s - a)(s - b)(s - c)}$
$\sqrt{22(22 - 18)(22 - 14)(22 - 12)}$
$\sqrt{22 \times 4 \times 8 \times 10}$
$\sqrt{2 \times 11 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5}$

(Make Pairs of same digits )

$2 \times 2 \times 2 \sqrt{11 \times 2 \times 5}$
$8 \sqrt{110}$
$8 \times 10.488$
$= 83.904cm {}^{2}$




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Answer 2

• $16 \sqrt{55} cm {}^{2}$

Step-by-step explanation:

• sides are 9x+7x+6x =44cm
• 9+7+6=22x = 44
• x=44/22
• x=2
• 9x = 9×x = 9×2 = 18
• 7x = 7×x = 7×2 = 14
• 6x=7×x=7×2 = 12
• a= 18cm, b=14cm, c=12cm
• perimeter is 18+14+12=44
• 44/2 s=22
• area of ️le=
• $\sqrt{22(22 - 18)(22 - 14)(22 - 12)}$
• $\sqrt{22 \times 4 \times 8 \times 10}$
• $2 \sqrt{11 \times 2 \times 4 \times 2 \times 5 \times 2}$
• $2 \times 4 \times 2\sqrt{11 \times 5}$
• $16\sqrt{55} cm {}^{2}$