1.

The sides of a triangle are in the ratio 4:5:7. If the perimeter of the triangle is 32cm Find the area of the Triangle.​

Answer»

GIVEN :-

  • Ratio of triangle are in ratio 4:5:7.
  • PERIMETER of the triangle is 32cm.

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TO FIND :-

  • Area of the triangle.

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SOLUTION :-

Let the sides of the triangle be 4x , 5x and 7x respectively as ratio is 4:5:7.

Perimeter = Sum of all sides

→ 32 = 4x + 5x + 7x

→ 32 = 16x

→ x = 32/16

→ x = 2

Sides are :-

  • 4x = 4(2) = 8cm
  • 5x = 5(2) = 10cm
  • 7x = 7(2) = 14cm

Hence , sides of the triangle are 8cm , 10cm and 14cm. Perimeter is 32cm.

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For area ,

\\ \boxed{\sf \: area = \sqrt{s(s - a)(s - b)(s - c)} } \\

Here ,

  • s → Semi-perimeter
  • a ,b ,c → Sides of triangle

We have,

  • s = 32/2 = 16cm
  • a = 8cm
  • b = 10cm
  • c = 14cm

Putting values we GET,

\\ \sf \: area = \sqrt{16(16 - 8)(16 - 10)(16 - 14)} \\ \\ \sf \: area = \sqrt{16(8)(6)(2)} \\ \\ \sf \: area = \sqrt{1536} \\ \\ \boxed{\sf \: area = 39.2 {cm}^{2} } \\

Hence , area of triangle is 39.2cm².


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