Question

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

Answer 1

Given :

• Sides of traingle are in Ratio 25: 17: 12.
• Perimeter of Traingle is 540m

To find :

• Area of Traingle

Solution :

• In the question Perimeter of Field Is 540m. So, Firstly we will find the sides of the Traingle. let the sides be 25x ,17x and 12x.

• After Finding the sides of traingle. we will find the Area of Traingle using the Heron's Formula

✪ Let 1st side (a) = 25x

✪ 2nd side (b) = 17x

✪ 3rd side (c) = 12x

_______________

Let's Find out...!

Perimeter of Traingle = a + b + c

➤ 540 = 25x + 17x + 12x

➤ 540 = 42x + 12x

➤ 540 = 54x

➤ x = 540/54

➤ x = 10

_______________

Now,Finding sides

✪ 1st Side = 25x = 250m

✪ 2nd Side = 17x = 170m

✪ 3rd Side = 12x = 120m

Side = a + b + c/2

➤ 250 + 170 + 120/2

➤ 540/2

➤ 270m

Now, Finding Area of Traingle

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

➤ √270 (270 - 250)(270 - 170)(270 - 120)

➤ √270(20 × 100 × 150)

➤ √81,000,000

➤ √9000 × 9000

➤ 9000

_______________

∴ Area of Traingle is 9000m²

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Answer 2

Given :

• Perimeter of Triangular field = 540m
• Ratio of sides of field = 25:17:12

To Find :

• Area of Triangular field.

Solution :

✰ In this question, the ratio of sides and perimeter of Triangular field are given. So firstly we will find the sides of the triangular field and then we will find the semi perimeter of the Triangular field after that we will use Heron's Formula to find the area of Triangular field.

⠀⠀

➞ Let the first side be 25p

➞ Let the second side be 17p

➞ Let the third side be 12p

⠀⠀⠀

⠀⠀⠀⟼⠀⠀⠀Perimeter of Field = 540

⠀⠀⠀⟼⠀⠀⠀25p + 17p + 12p = 540

⠀⠀⠀⟼⠀⠀⠀25p + 29p = 540

⠀⠀⠀⟼⠀⠀⠀54p = 540

⠀⠀⠀⟼⠀⠀⠀p = 540/54

⠀⠀⠀⟼⠀⠀⠀p = 10m

⠀⠀

Now,

➣ First Side (a) = 25p

➣ First Side (a) = 25 × 10

➣ First Side (a) = 250m

⠀

➣ Second Side (b) = 17p

➣ Second Side (b) = 17 × 10

➣ Second Side (b) = 170m

⠀

➣ Third Side (c) = 12p

➣ Third Side (c) = 12 × 10

➣ Third Side (c) = 120m

⠀

________________

✰ Now, We will find the semi perimeter of the Triangular field.

⠀⠀⠀⟼⠀⠀⠀s = a + b + c/2

⠀⠀⠀⟼⠀⠀⠀s = 250 + 170 + 120/2

⠀⠀⠀⟼⠀⠀⠀s = 250 + 290/2

⠀⠀⠀⟼⠀⠀⠀s = 540/2

⠀⠀⠀⟼⠀⠀⠀s = 270m

⠀

✰ Now, We will find the area of the Triangular field using Heron's Formula.

➟ √s (s - a) (s - b) (s - c)

➟ √270(270 - 250)(270 - 170)(270 - 120)

➟ √270 × 20 × 100 × 150

➟ √5400 × 15000

➟ √81000000

➟ 9000m²

Thus Area of Triangular field is 9000m²

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