Question

The sides of a triangle are in the ratio 3:4:5, The perimeter is 120 cm, The area of the triangle is? (No Inappropriate Answer)

Answer 1

Step-by-step explanation:

Lets make them fractions

3/12, 4/12, 5/12

All of them make 120cm

120× 3/12= 360/12 = 30cm

120 × 4/12 = 480/12 = 40 cm

120 × 5/12 = 600/12 = 50cm

Answer 2

Answer :

• 600 cm²

Given :

• The sides of Triangle = 3:4:5
• Perimeter = 120 cm

To find :

• the area of the triangle

Solution :

⇒ Let's find the sides. Let the sides be 3x, 4x, and 5x.

$\sf \rightarrow a + b +c = 120$

$\sf \rightarrow 3x + 4x + 5x = 120$

$\sf \rightarrow 12x = 120$

$\sf \rightarrow x = \dfrac{120}{12}$

$\sf \to x = \cancel{\dfrac{120}{12}}$

$\sf \to x = 10$

→ Sides :

$\sf \to 3x = 3 \times 10 = 30 cm$

$\sf \to 4x = 4 \times 10 = 40 cm$

$\sf \to 5x = 5 \times 10 = 50 cm$

• Therefore, the sides of the triangle are 30 cm, 40 cm, and 50 cm.

⇒ Now, let's find the area of the Triangle.

$\sf$$\sf Semi-Perimeter = \dfrac{a + b + c}{2}$

$\sf = \dfrac{30 + 40 + 50}{2}$

$\sf = \dfrac{120}{2}$

$\sf = \cancel {\dfrac{120}{2}}$

$\sf = 60 cm$

$\sf \to Area= \sqrt{s (s - a) (s - b) (s -c)}$

$\sf = \sqrt{60 (60 -30) (60 - 40) (60 - 50)}$

$\sf = \sqrt{60 (30) (20) (10)}$

$\sf = \sqrt{60 \times (30) \times (20) \times (10)}$

$\sf = \sqrt{360000}$

$\sf = 600$

• Therefore, the area of the triangle is 600 cm².