Question

The perimeter of a triangle is 480 metres and its sides are in the ratio of 1:2:3 find the area of triangle in the lesson Heron's Formula. please answer it correctly​ wrong answer will be reported

Answer 1

Given :-

• Perimeter of a triangle = 480 m
• Ratio of the sides of the triangle = 1 : 2 : 3

To find :-

• Area of triangle

Knowledge required :-

• Formula to calculate perimeter of triangle :-

Perimeter of triangle = sum of its all sides

• Formula to calculate Semi - perimeter (s) :-

⠀⠀⠀ s = (a + b + c)/2

• Heron's formula :-

⠀⠀⠀= √s(s - a)(s - b)(s - c)

~Understanding the concept ::

Here, we have to find the area of the triangle by using Heron's formula. For that firstly, we will find all the sides of the triangle by using the formula of perimeter of triangle. And then we will substitute the value of the sides in the formula of semi - perimeter, heron's formula. From there we will get the value of the area of the triangle.

Solution :-

Let the three sides of the triangle be 1x, 2x and 3x.

• First side = 1x
• Second side = 2x
• Third side = 3x

Perimeter = sum of all sides.

⠀⠀⠀⇒ 480 = 1x + 2x + 3x

⠀⠀⠀⇒ 480 = 6x

⠀⠀⠀⇒ 480/6 = x

⠀⠀⠀⇒ 80 = x

The value of x = 80.

Substitute the value of x in the side which we have let.

• First side = 1x = 80 m
• Second side = 2x = 2 × 80 = 160 m
• Third side = 3x = 3 × 80 = 240 m

Semi - perimeter (s) = (a + b + c)/2

Take,

• a = 80 m
• b = 160 m
• c = 240 m

⠀⠀⠀⇒ s = (80 + 160 + 240)/2

⠀⠀⠀⇒ s = 480/2

⠀⠀⠀⇒ s = 240

Semi - perimeter of the triangle = 240 m

Heron's formula = √s(s - a)(s - b)(s - c)

⠀⠀⠀⇒ √240(240 - 180)(240 - 160)(240 - 240)

⠀⠀⠀⇒ √240(60)(80)(0)

⠀⠀⠀⇒ √240(0)

⠀⠀⠀⇒ 0

★ Area of the triangle = 0 m²

Answer 2

Given :-

Perimeter of a triangle = 480 m

Ratio of the sides of the triangle = 1 : 2 : 3

To find :-

Area of triangle

Knowledge required :-

Formula to calculate perimeter of triangle :-

Perimeter of triangle = sum of its all sides

Formula to calculate Semi - perimeter (s) :-

⠀⠀⠀ s = (a + b + c)/2

Heron's formula :-

⠀⠀⠀= √s(s - a)(s - b)(s - c)

~Understanding the concept ::

Here, we have to find the area of the triangle by using Heron's formula. For that firstly, we will find all the sides of the triangle by using the formula of perimeter of triangle. And then we will substitute the value of the sides in the formula of semi - perimeter, heron's formula. From there we will get the value of the area of the triangle.

Solution :-

Let the three sides of the triangle be 1x, 2x and 3x.

First side = 1x

Second side = 2x

Third side = 3x

Perimeter = sum of all sides.

⠀⠀⠀⇒ 480 = 1x + 2x + 3x

⠀⠀⠀⇒ 480 = 6x

⠀⠀⠀⇒ 480/6 = x

⠀⠀⠀⇒ 80 = x

The value of x = 80.

Substitute the value of x in the side which we have let.

First side = 1x = 80 m

Second side = 2x = 2 × 80 = 160 m

Third side = 3x = 3 × 80 = 240 m

Semi - perimeter (s) = (a + b + c)/2

Take,

a = 80 m

b = 160 m

c = 240 m

⠀⠀⠀⇒ s = (80 + 160 + 240)/2

⠀⠀⠀⇒ s = 480/2

⠀⠀⠀⇒ s = 240

Semi - perimeter of the triangle = 240 m

Heron's formula = √s(s - a)(s - b)(s - c)

⠀⠀⠀⇒ √240(240 - 180)(240 - 160)(240 - 240)

⠀⠀⠀⇒ √240(60)(80)(0)

⠀⠀⠀⇒ √240(0)

⠀⠀⠀⇒ 0

★ Area of the triangle = 0 m²