Question

4. The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is
144 cm. Find the area of the triangle.
​

Answer 1

Answer:

Let the sides = 3x , 4x, 5x

3x +4x+ 5x= 144cm

12x=144

x= 144/12

x= 12

3x= 3×12= 36cm

4x= 4×12=48cm

5x= 5×12= 60cm

Area of triangle =

√s(s−a)(s−b)(s−c)

s=72 and a=36, b=48 c=60

√72(36)(24)(12)

√746496

area of triangle is 864 cm

Step-by-step explanation:

PLEASE MARK ME AS A BRAINLIEST

Answer 2

AnswEr :-

• Area of the triangle is 864cm².

Given :-

• The lengths of the sides of a triangle are in the ratio 3:4:5 and it's perimeter is 144cm.

To Find :-

• Area of the triangle.

SoluTion :-

Put x in the ratio.

Then, sides are :-

• 3x
• 4x
• 5x

Given that,

• Perimeter of the triangle is 144cm.

We know that the perimeter of a triangle is :-

• sum of all sides

According to question :-

3x + 4x + 5x = 144

→ 7x + 5x = 144

→ 12x = 144

→ x = 144/12

→ x = 12

Now,

Sides are

• 3x = 3 × 12 = 36
• 4x = 4 × 12 = 48
• 5x = 5 × 12 = 60

Semi Perimeter (S) = 144/2 = 72

We know that the area of a triangle is

• √s (s -a) (s - b) (s - c)

According to question :-

√ 72 (72 - 36) (72 - 48) (72 - 60)

→ √ 72 × 36 × 24 × 12

→ √ 746496

→ √ 864 × 864

→ 864 cm²

Hence, the area of the triangle is 864cm².

_____________________

________________________________