Question

The sides of a triangular plot are in the ratio 13 : 12 : 5 and its perimeter is 450 metre.Find the area of the triangular plot.​

Answer 1

$\huge\star\underline\mathfrak\red{Answer:-}$

6750 m²

Step-by-step explanation:

Given Perimeter = 450 m.

Semi-Perimeter (s) = Perimeter/2

                               = 450/2

                               = 225 m.

Given ratio of sides is 13:12:5.

Let sides be a = 13x, b = 12x, c = 5x.{x be any number}

Now,

Perimeter = 450 m.

⇒ a + b + c = 450

⇒ 13x + 12x + 5x = 450

⇒ 30x = 450

⇒ x = 15

So,

⇒ 13x = 195 m.

⇒ 12x = 180 m.

⇒ 5x = 75 m.

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

                             = √225(225 - 195)(225 - 280)225 - 75)

                             = √225(30)(45)(150)

                             = √45562500

                             = 6750 m²

Therefore, Area of triangle = 6750 m²

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Answer 2

$\huge\star\underline\mathfrak\red{Answer:-}$

6750 m²

Step-by-step explanation:

Given Perimeter = 450 m.

Semi-Perimeter (s) = Perimeter/2

                               = 450/2

                               = 225 m.

Given ratio of sides is 13:12:5.

Let sides be a = 13x, b = 12x, c = 5x.{x be any number}

Now,

Perimeter = 450 m.

⇒ a + b + c = 450

⇒ 13x + 12x + 5x = 450

⇒ 30x = 450

⇒ x = 15

So,

⇒ 13x = 195 m.

⇒ 12x = 180 m.

⇒ 5x = 75 m.

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

                             = √225(225 - 195)(225 - 280)225 - 75)

                             = √225(30)(45)(150)

                             = √45562500

                             = 6750 m²

Therefore, Area of triangle = 6750 m²