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.