Question

The side of a triangle are in the ratio of 3:5:7 and it's perimeter is 150m. Find its area using heron 's formula
Fast please ​

Answer 1

• Area of triangle is 648.75 m².

Step-by-step explanation:

Given:-

• Sides of triangle are in ratio of 3:5:7.
• Perimeter of triangle is 150 m.

To find:-

• Area of triangle.

Solution:-

Let, Sides of triangle be 3x, 5x and 7x.

Perimeter of triangle = Sum of all sides

$\longrightarrow$ 3x + 5x + 7x = 150

$\longrightarrow$ 15x = 150

$\longrightarrow$ x = 150/15

$\longrightarrow$ x = 10

So,

Sides are :

3x = 3×10 = 30 m

5x = 5×10 = 50 m

7x = 7×10 = 70 m

Now,

Semi-perimeter = Perimeter/2

= 150/2

= 75

Semi-perimeter is 75 m.

According to question :

$\sf \longrightarrow Area_{(Triangle)} =$ √75 × (75 - 30)(75 - 50)(75 - 70)

$\sf \longrightarrow Area_{(Triangle)} =$ √75 × 45 × 25 × 5

$\sf \longrightarrow Area_{(Triangle)} =$ √5×5×3×5×3×3×5×5×5

$\sf \longrightarrow Area_{(Triangle)} =$ 5 × 5 × 5 × 3 × √3

$\sf \longrightarrow Area _{(Triangle)}=$ 375 × √3

• √3 is irrational number. Value of √3 is 1.73.

$\sf \longrightarrow Area_{(Triangle)} =$ 375 × 1.73

$\longrightarrow \purple{\boxed{\sf \bold{Area_{(Triangle)} = 648.75}}\star}$

Therefore,

Area of triangle is 648.75 m².