Question

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.

Answer 1

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

Let the sides be a = 25x , b = 17x and c = 12x .

Perimeter of ∆ = a + b + c  

⇒ 540 = 25x + 17x + 12x

⇒ 54x = 540

⇒ x = 540/54

⇒ x = 10

So the Sides of a triangle are :  

a = 25x = 25 × 10 = 250 m

b = 17x = 17 × 10 = 170 m

c = 12x = 12 × 10 = 120 m

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

Semi-perimeter (s) = (250 + 170 + 120)/2

s = 540/2  

s = 270 m

Using Heron’s formula :  

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

A = √270(270 - 250)(270 - 170)(270 - 120)

A = √270 × (20) × (100) × (150)

A = √(9 × 3 × 10) × (2 × 10) × (10 × 10) × (10 × 15)

A = √(10 × 10 × 10 × 10) × 10 × (9) × (3) × (2) × (3 × 5)  

A = √(10 × 10 × 10 × 10) × (2 × 5) × (9) × (3) × (2) × (3 × 5)  

A = √(10 × 10 × 10 × 10) × (2 × 2) × (3 × 3) × (3 × 3) × (5 × 5)  

A = 10 × 10 × 2 × 3 × 3 × 5

A = 100 × 90

A = 9000 m²

Hence, the area of triangle is 9000 m²

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Answer 2

Answer:

Step-by-step explanation:

Given :-

Perimeter of triangular field = 540 m

Ratio of sides = 25 : 17 : 12.

To Find :-

Area of a triangle.

Formula to be used :-

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

Solution :-

⇒ 25x + 17x + 12x = 540 m  

⇒ 54x = 540 m  

⇒ x = 540/54

⇒ x = 10 m

The sides of a triangle are  a = 250 m  b = 170 m  c = 120 m and s = 270 m

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

⇒ Area of the triangle = √ S(S - 250)(S - 170)(S - 120)

⇒ Area of the triangle = √ 270(270 - 250)(270 - 170)(270 - 120)

⇒ Area of the triangle = √ 270× 20×100×150

⇒ Area of the triangle  = √ 81000000

⇒ Area of the triangle = 9000 m²

Hence, the area of a triangle is 9000 m².