Question

the length of side of a triangle are int the ratio 4:5:3 and it perimeter is 96cm find it area​

Answer 1

Answer:

384 cm²

Step-by-step explanation:

Let the sides of the triangle be 4x cm, 5x cm and 3x cm.

It is given that the perimeter of the triangle is 96 cm.

Therefore,

→ 4x + 5x + 3x = 96

→ 12x = 96

→ x = 96/12

→ x = 8

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Now, the sides of the triangle are :

1st side = a = 4x = 4(8) = 32 cm

2nd side = b = 5x = 5(8) = 40 cm

3rd side = c = 3x = 3(8) = 24 cm

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Let's find out if the triangle is a right - angles triangle or not.

It can be find out using Pythagoras Theorem.

→ (Hypotenuse)² = (Base)² + (Perpendicular)²

Let, the bigger side be hypotenuse and the other two sides be base and perpendicular.

→ (40)² = (32)² + (24)²

→ 1600 = 1024 + 576

→ 1600 = 1600

Hence, the triangle is a right - angles triangle.

Applying formula :

Area of triangle = 1/2 × Base × Perpendicular

→ 1/2 × 32 × 24

→ 32 × 12

→ 384 cm²