Question

The sides of a triangle are in the ratio of 3:4:5. If its perimeter is 36 cm, then What is its area?​

Answer 1

Step-by-step explanation:

Given :

Sides ratio = 3:4:5

Let the Length of sides = x

⇒ Sides = 3x , 4x , 5x

Perimeter = 36cm

Perimeter = a + b + c

⇒ 36cm = 3x + 4x + 5x

⇒ 36cm = 12x

Transposing The Terms

⇒ x = 36cm/12

∴ x = 3cm

Sides -

⇒ 3x = 3(3) = 9cm

⇒ 4x = 4(3) = 12cm

⇒ 5x = 5(3) = 15cm

Since,

15² = 12² + 9²

we can consider it right angled triangle.

Area = 1/2 × base × height

⇒ Area = 1/2 × 12 × 9

⇒ Area = 6 × 9

∴ Area = 54cm²

Alternative Method

Semi - Perimeter-

s = a + b + c/2

⇒ s = 15 + 12 + 9/2

⇒ s = 36/2

s = 18cm

Herons Formula

Area = √s(s - a)(s - b)(s - c)

⇒ Area = √18(18 - 15)(18 - 12)(18 - 9)

⇒ Area = √18 × 3 × 6 × 9

⇒ Area = √3 × 3 × 6× 6 × 3 × 3

⇒ Area = 6 × 3 × 3

Area = 54 cm²

Answer 2

Answer:

The area of triangle is 54 cm².