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The sides of a triangle are in the ratio of 3:4:5 if its perimeter is 84 cm, then what is its area

User ChatterOne
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Solution :

Let's assume,

  • side a = 3x
  • side b = 4x
  • side c = 5x

We know that perimeter of triangle is sum of all the sides.

a + b + c = Perimeter

3x + 4x + 5x = 84

12x = 84

x = 84/12

x = 7

Hence,

  • side a = 3x = 3(7) = 21 cm
  • side b = 4x =4(7) = 28 cm
  • side c = 5x = 5(7) = 35 cm

Now,

Semi-perimeter = Perimeter/2

= 84/2

= 42 cm

Using heron's formula,

  • Area = s√s - a)(s -b)(s -c)

Where,

  • s is semi-perimeter
  • a, b and c are sides of triangle.

= √42(42- 21)(42 ; 28)(42- 35)

= √42( 21 × 14 × 7)

= √42 × 2058

= √ 86,436

= 294 cm²

Therefore, Area of the triangle is 294 cm²

User Waqas Ashraf
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