the sides f a triangular field are in the ratio of 5:3:4 and its perimeter 180m.find its area

180 / (5 + 3 + 4) = 15

5 * 15 = 75
3 + 15 = 45
4 * 15 = 60

3 * 15 = 45

MATHMATIC

To find the area of a triangular field, we need to know the lengths of its sides. Given that the sides of the triangular field are in the ratio of 5:3:4, let's assume that the lengths of the sides are 5x, 3x, and 4x, where x is a common factor.

We know that the perimeter of the triangular field is 180 meters, so we can write an equation:

5x + 3x + 4x = 180

Combining like terms, we get:

12x = 180

Divide both sides of the equation by 12:

x = 180 / 12

Simplifying, we find:

x = 15

Now we can find the lengths of the sides:

Side 1 = 5x = 5 * 15 = 75 meters
Side 2 = 3x = 3 * 15 = 45 meters
Side 3 = 4x = 4 * 15 = 60 meters

To find the area of the triangular field, we can use Heron's formula, which states that the area of a triangle with sides a, b, and c, where s is the semi-perimeter (s = (a + b + c) / 2), is given by:

Area = √(s(s - a)(s - b)(s - c))

Let's calculate the area using the lengths of the sides:

s = (75 + 45 + 60) / 2 = 90 (semi-perimeter)

Area = √(90(90 - 75)(90 - 45)(90 - 60)) ≈ √(90 * 15 * 45 * 30)

Calculating this expression gives the area of the triangular field.