Q.13 The sides of a triangle are in the ratio of 3:4:5. If its perimeter is 36 cm, then What is its area?
Answers
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
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
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