Question

the
perimeter of triangular
is 450 m. and its sides
field are in the ratio13:12:5. Find the area of the triangle.
​

Answer 1

Refer The Attachment ⬆️

• $\boxed{\pink{\sf{s = \frac{a+b+c}{2}}}}$

where 's' is the Semi Perimeter.

• $\boxed{\red{\sf{Area\;of\;∆le = \sqrt{s(s-a)(s-b)(s-c)}}}}$

It is known as Heron's Formula.

Area of ∆le ➝ 6750m²

$\Large{✓}$

Hope It Helps You ✌️

Answer 2

Appropriate Question :

The perimeter of triangular field is 450 m and the sides of the field are in the ratio 13:12:5. Find the area of the trianglular field.

Given :

• Perimeter of the triangular field = 450 m

• Ratio of the sides of triangular field = 13 : 12 : 5

To find :

• Area of the triangular field = ?

Solution :

Let,

• The first side of the triangular field = 13x
• The second side of the triangular field = 12x
• The third side of the triangular field = 5x

Using formula,

⟶ Perimeter of triangle = a + b + c

where,

• a, b and c are the three sides of the triangle

Sunstituting the given values ::

⟶ 450 = 13x + 12x + 5x

⟶ 450 = 30x

⟶ 450/30 = x

⟶ 45/3 = x

⟶ 15 = x

Substituting the value of x :-

⟶ First side = 13x

⟶ First side = 13 × 15

⟶ First side = 195 m

⟶ Second side = 12x

⟶ Second side = 12 × 15

⟶ Second side = 180 m

⟶ Third side = 5x

⟶ Third side = 5 × 15

⟶ Third side = 75 m

Now, calculating the area of the triangular field :-

Using formula,

⟶ Semi perimeter = Periemter ÷ 2

⟶ Substituting the given values :-

⟶ Semi perimeter = 450 ÷ 2

⟶ Semi perimeter = 225 m

Using formula,

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

⟶ Substituting the given values :-

⟶ Area = √225(225 - 195)(225 - 180)(225 - 75)

⟶ Area = √225(30)(45)(150)

⟶ Area = √45,562,500

⟶ Area = ± 6750

As we know, the area of triangle cannot be negative. So, the negative sign will get rejected.

⟶ Area = 6750

Therefore, the area of triangular field = 6750 m²