1
The sides of a triangle are in the ratio of 5 : 4 : 3. If its perimeter is 24 cm, what is the area of the triangle?
- A12 cm2
- B24 cm2
- C6 cm2
- D48 cm2
Answer not set
Discussion 1
Log in or create a free account to reply and vote.
0
CCommunity
Let the sides of triangle be 5x, 4x and 3x respectively
Perimeter= 24 (given)
⇒ 5x + 4x + 3x =24
⇒ 12x = 24
⇒ x = 2
∴ Sides of triangle become 5 × 2 = 10, 4 × 2 =8, 3 × 2 = 6
Now as we observe these sides satisfy the Pythagoras theorem,
i.e. (10)2 = (6)2 + (8)2
∴ there is a right angle in the triangle
So Area = (1/2) × base × height
= (1/2) × 6 × 8
= 48/2
= 24 sq. Cm
Perimeter= 24 (given)
⇒ 5x + 4x + 3x =24
⇒ 12x = 24
⇒ x = 2
∴ Sides of triangle become 5 × 2 = 10, 4 × 2 =8, 3 × 2 = 6
Now as we observe these sides satisfy the Pythagoras theorem,
i.e. (10)2 = (6)2 + (8)2
∴ there is a right angle in the triangle
So Area = (1/2) × base × height
= (1/2) × 6 × 8
= 48/2
= 24 sq. Cm