Question

The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle.

Answer 1

Given : The perimeter of a triangular field is 300 m and its sides are in the ratio 3 : 5 : 7.

Let the sides be a = 3x , b = 5x and c = 7x .

Perimeter of ∆ = a + b + c  

⇒ 300 = 3x + 5x + 7x

⇒ 15x = 300

⇒ x = 300/15

⇒ x = 20

So the Sides of a triangle are :  

a = 3x = 3 × 20 = 60 m

b = 5x = 5 × 20 = 100m

c = 7x = 7 × 20 = 140m

Semi Perimeter of the ∆,s = (a + b + c) /2

Semi-perimeter (s) = (60 + 100 + 140)/2

s = 300/2  

s = 150 m

Using Heron’s formula :  

Area of the wall , A = √s (s - a) (s - b) (s - c)

A = √150(150 -  60)(150 - 100)(150 - 140)

A = √150 × (90) × (50) × (10)

A = √(10 × 15) (9 × 10) × (5 × 10) × 10  

A = √(10 × 10 × 10 × 10) × (5 × 3)  × (9) × 5

A = √(10 × 10 × 10 × 10) × (5 × 5) × (3 × 3) × 3

A = 10 × 10 × 5 × 3 √3

A = 1500√3 m²

Hence, the area of the triangle  is 1500√3 m².

HOPE THIS ANSWER WILL HELP YOU…..

Similar questions :

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of a triangle.

https://brainly.in/question/15908213

 

Find the area of a triangle whose sides are respectively 150 cm, 120 cm, and 200 cm.

https://brainly.in/question/15908186

Answer 2

Answer:

Step-by-step explanation:

Given :-

Perimeter of triangle = 300 m

Ratio of sides = 3 : 5 : 7

To Find :-

Area of the triangle.

Formula to be used :-

Area of the triangle = √s(s - a)(s - b)(s - c)

Solution :-

Let the sides be 3x, 5x and 7x.

⇒ 3x + 5x + 7x = 300

⇒ 15x = 300

⇒ x = 300/15

⇒ x = 20

s = 150,  a = 60,  b = 100,  c = 140

Area of the triangle = √s(s - a)(s - b)(s - c)

⇒ Area of the triangle = √150(150 - 60)(150 - 100)(150 - 140)

⇒ Area of the triangle =  √150 (90) (50) (10)

​⇒ Area of the triangle = 1500√3 m²  

Hence, the area of the triangle is 1500√3 m²  .