Question

and perimeter is 42cm.
2. The sides of a triangle are in the ratio 5:12:13 and its perimeter is
150 m. Find the area of the triangle.

Answer 1

Given :

• The sides of a triangle are in the ratio 5:12:13.
• Perimeter of the Triangle = 150m

To Find :

• Area of Triangle

Solution :

Let,

• First Side of Triangle = 5x
• Second Side of Triangle = 12x
• Third Side of Triangle = 13x

Finding the sides of triangle :

⠀⟿⠀Perimeter = Sum of all sides

⠀⟿⠀150 = 5x + 12x + 13x

⠀⟿⠀150 = 5x + 25x

⠀⟿⠀150 = 30x

⠀⟿⠀150/30 = x

⠀⟿⠀5 = x

Therefore :

• First Side of Triangle = 5x
• First Side of Triangle = 5 × 5
• First Side of Triangle = 25m

• Second Side of Triangle = 12x
• Second Side of Triangle = 12 × 5
• Second Side of Triangle = 60m

• Third Side of Triangle = 13x
• Third Side of Triangle = 13 × 5
• Third Side of Triangle = 65m

___________________

Finding the Semi Perimeter :

⠀⟿⠀Semi Perimeter = a + b + c/2

⠀⟿⠀Semi Perimeter = 25 + 60 + 65/2

⠀⟿⠀Semi Perimeter = 25 + 125/2

⠀⟿⠀Semi Perimeter = 150/2

⠀⟿⠀Semi Perimeter = 75m

Finding the Area :

Applying Heron's Formula :

⠀⟿⠀√s (s - a) (s - b) (s - c)

⠀⟿⠀√75 (75 - 25) (75 - 60) (75 - 65)

⠀⟿⠀√75 × 50 × 15 × 10

⠀⟿⠀√3750 × 150

⠀⟿⠀√562,500

⠀⟿⠀750m²

⛬ Area of Triangle is 750m²

___________________

Answer 2

Given :

• Perimeter of Traingle is 150cm
• Sides of traingle are in Ratio 5:12:13

To Find :

• Area of Traingle

Solution :

Here in the Question we are given Sides of traingle in ratio and perimeter is 150m. So, Firstly we will find the side of triangle. Formula of Area of Triangle is √s (s - a)(s - b)(s - b). By Putting the values in the formula we can easily find the Area of Traingle.

______________

Let Sides of traingle be

• 1st side (a) = 5x
• 2nd side (b) = 12x
• 3rd side (c) = 13x

Perimeter of Traingle = 150m

→ a + b + c = 150

→ 5x + 12x + 13x = 150

→ 30x = 150

→ x = 150/30

→ x = 5

Now, sides of traingle

• 1st Side = 5x = 5*5 = 25m
• 2nd Side = 12x = 12*5 = 60m
• 3rd Side = 13x = 13*5 = 65m

Semi Perimeter = a + b + c/2

→ 25 + 60 + 65/2

→ 150/2 = 75m

Area of Traingle = √s (s - a)(s - b)(s - b)

→ √75 (75 - 25)(75 - 60)(75 - 65)

→ √75 × 50 × 15 × 10

→ √562500

→ 750 m²

∴ Area of Traingle is 750m²