Question

The sides of a triangle are in the ratio 3 : 4 : 5. If perimeter of the
triangle in 360m, find its area using Heron’s formula.

Answer 1

Answer:

3x plus 4x plus 5x is equal to 360

12x is equal to 360

Answer 2

• Area of triangle is 5400 m².

Step-by-step explanation:

Given:-

• Sides of triangle are in ratio 3:4:5.
• Perimeter of triangle is 360 m.

To find:-

• Area of triangle.

Solution:-

Let, Sides of triangle be 3x, 4x and 5x.

Perimeter of triangle = a+b+c

• Where, a,b and c are sides of triangle.

Puting sides and perimeter of triangle.

$\longrightarrow$ 3x + 4x + 5x = 360

$\longrightarrow$ 12x = 360

$\longrightarrow$ x = 360/12

$\longrightarrow$ x = 30

Sides of triangle :-

3x = 3×30 = 90

4x = 4×30 = 120

5x = 5×30 = 150

Sides of triangle are 90m, 120m and 150m.

Area of triangle by using Heron's formula is :

Area of triangle = $\bold{\sqrt{s(s-a)(s-b)(s-c)}}$

Where,

• S is semi-perimeter of triangle.
• a, b and c are sides of triangle.

So,

Semi-perimeter = Perimeter/2

= 360/2

= 180

Semi-perimeter of triangle is 180 m.

Area of triangle:

$\longrightarrow$ √180(180 - 90)(180 - 60)(180 - 30)

$\longrightarrow$ √180 × 90 × 60 × 30

$\longrightarrow$ √29160000

$\longrightarrow \purple{\boxed{\sf \bold{ 5400}} \star}$

Therefore,

Area of triangle is 5400 m².