Question

the side of a triangle are in the ratio 3:4:5. if perimeter is 36cm find the area​

Answer 1

Given :

Sides of a Δle are in the ratio 3 : 4 : 5

So ,let the sides of the triangle be 3x, 4x and 5x

Perimeter of Δle = 36 cm

  ⇒ 3x + 4x + 5x = 36

                     12x = 36

                        x = 3

Substituting x in the sides, we get:

3x = 3(3) = 9cm

4x = 4(3) = 12cm

5x = 5(3) = 15cm

Hence, the sides of the Δle are 9cm, 12cm and 15cm.

Let's take a = 9, b = 12, c = 15

Here, to find the area, we apply Heron's formula

             Perimeter = 36

⇒Semi-perimeter = 36 ÷ 2 ⇒ s = 18cm

Area = √s (s-a) (s-b) (s-c)

        = √18 (18-9) (18-12) (18-15)

       = √18 × 9 × 6 × 3

      = 54cm²

Hence, the area of the Δle = 54cm²

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Answer 2

From given condition,

3x+4x+5x=36

12x=36

x=36/12

x=3

Sides of triangle are:

1. 3x=3×3=9

2.4x=4×3=12

3.5x=5×4=20

Here 3,4 and 5 are the pythagorean triplets.

Thus this traingle is a right angled triangle.

Area of right angled triangle =1/2 ×sides forming right angle

=1/2× 3×4

=1/2×12

=6 sq cm

Thus the area of triangle is 6 sq cm.

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