Question

30 Points!
Solve this with steps, please. Answer quickly with the required steps to win Brainliest answer.

The sides of a triangular field are in the ratio 5:3:4 and its perimeter is 180m.
Find the (i) Area, (ii) Altitude corresponding to the longest side and (iii) The cost of leveling the field at the rate of Rs. 10 per square metre.

Answer 1

Step-by-step explanation:

let the sides of the triangle be 5x m , 3x m and 4x m

perimeter = 180 m

atp ,

5x + 3x + 4x = 180

12 x = 180

there fore ,

x = 180 / 12 = 15 m

Answer 2

Ratio of sides of triangle is given as 5:3:4

let the sides are 5x, 3x, 4x

according to the question the perimeter is 180m.

Therefore,

5x + 3x +4x = 180

x = 15

the sides are,

5 × 15 = 75

3 × 15 = 45

4 × 15 = 60

{i} Area

By using Herons formula

$area = \sqrt{s(s - a)(s - b)(s -c )}$

where,

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

$s = \frac{a + b + c}{2}$

Area => 1,350 m²

{ii} Altitude corresponding to the longest side

Area of triangle is =

$\frac{1}{2} \times base \times altitude$

base = 75

1350 = 1/2 × 75 × altitude

Altitude = 36 m

{iii} Cost of leveling the ground

per meter square = 10 ₹

1350 meter square = 1350 × 10 = 13500₹