Question

2. The lengths of the sides of a triangle are in
the ratio 3 : 4 : 5. Find the area of the trian-
gle if its perimeter is 144 cm.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer

• The area of the triangle is 864 cm²

Explanation

Given

• The sides of a triangle are of the ratio 3:4:5
• Perimeter of the triangle is 144 cm

To Find

• Area of the triangle?

Solution

• First find the three sides assuming them to be 3x , 4x & 5x. Then use the Heron's formula to find the area of the triangle!!

✭ Value of x

→ Perimeter = Sum of all sides

→ 144 = 3x+4x+5x

→ 144 = 12x

→ 144/12 = x

→ x = 12

✭ Length of its sides

• 3x = 3×12 = 36cm = a
• 4x = 4×12 = 48cm = c
• 5x = 5×12 = 60cm = c

✭ Semi Perimeter

→ Semi Perimeter = Perimeter/2

→ Semi Perimeter = 144/2

→ Semi Perimeter = 72

✭ Area of the triangle

→ Area(∆) = √{s(s-a)(s-b)(s-c)}

→ Area(∆) = √{72(72-36)(72-48)(72-60)}

→ Area(∆) = √{72 × 36 × 24 × 12}

→ Area(∆) = √746496

→ Area(∆) = 864 cm²