Question

The perimeter of the triangle is 44 cm. If its sides are in the ratio 9:7:6 find its area. ​

Answer 1

Answer:-

$\red{\bigstar}$ Area of the Triangle $\large\leadsto\boxed{\tt\purple{83.90 \: cm^2}}$

• Given:-

• Perimeter of the triangle = 44 cm

• Ratio of the sides of triangle = 9:7:6

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• To Find:-

• Area of the triangle

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• Solution:-

• Let the sides of the triangle in ratio be 9x , 7x and 6x respectively.

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Now, The perimeter is 44 cm.

We know,

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\red{Perimeter = a+b+c}}}$

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➠ $\sf 44 = 9x + 7x + 6x$

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➠ $\sf 44 = 16x + 6x$

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➠ $\sf 44 = 22x$

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➠ $\sf x = \dfrac{44}{22}$

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★ $\large{\bf\pink{x = 2}}$

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Hence, sides are

9x = 9 × 2 = 18 cm

7x = 7 × 2 = 14 cm

6x = 6 × 2 = 12 cm

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Now,

We need to find the Area of the triangle.

We know,

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• Heron's Formula:-

$\pink{\bigstar}$ $\underline{\boxed{\bf\red{Area = \sqrt{s(s-a)(s-b)(s-c)}}}}$

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Firstly, we need to find the semi - perimeter (s),

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✴ $\underline{\boxed{\bf\green{Semi-Perimeter = \dfrac{Perimeter}{2}}}}$

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➠ $\sf Semi-Perimeter = \dfrac{44}{2}$

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★ Semi-Perimeter = 22 cm

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• Substituting in the Heron's Formula:-

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➠ $\sf Area = \sqrt{s(s-a)(s-b)(s-c)}$

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➠ $\sf Area = \sqrt{22(22-18)(22-14)(22-12)}$

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➠ $\sf Area = \sqrt{22 \times 4 \times 8 \times 10}$

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➠ $\sf Area = \sqrt{88 \times 80}$

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➠ $\sf Area = \sqrt{7040}$

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★ $\large{\bf\pink{83.90 \: cm^2}}$

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Therefore, the Area of the given triangle is 83.90 cm².

Answer 2

Given,

Perimeter of the triangle = 44cm

Ratio of sides = 9:7:6

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

Perimeter of triangle = a+b+c

44 = 9x+7x+6x

44 = 22x

x = 44/22

x = 2

The sides are : 9x=9×2=18 , 7x=7×2=14 and 6x=6×2=12

Now,

S = a+b+c/2

S = 18+14+12/2

S = 44/2

S = 22 cm

Area of triangle by Heron's Formula:

$area = \sqrt{s \times (s - a)(s - b)(s - c)} \\ = \sqrt{22(22 - 18)(22 - 14)(22 - 12)} \\ = \sqrt{22(4)(8)(10)} \\ = \sqrt{7040} \\ = 83.90$