Question

the ratio of the measures of three sides of a triangle is 4 ratio 2 ratio 3 and its perimeter is 36 cm find the area of the triangle​

Answer 1

Answer:

Hence, the area of the triangle is 46.44 cm².

Step-by-step explanation:

Given : The lengths of the sides of a triangle are in the ratio 4 : 2 : 3 and its perimeter is 36 cm.

To find : Area of the triangle​

Solution:

Let the sides be a = 4x , b = 2x and c = 3x .

Perimeter of ∆ = a + b + c  

⇒ 36 = 4x + 2x + 3x

⇒ 9x = 36

⇒ x = 36/9

⇒ x = 4

So , the Sides of a triangle are :  

a = 4x = 4 × 4 = 16 cm

b = 2x = 2 × 4 = 8 cm

c = 3x = 3 × 4 = 12 cm

Semi Perimeter of the ∆,s = (a + b + c) /2

Semi-perimeter (s) = (16 + 8 + 12)/2

s = 36/2  

s = 18 cm

Using Heron’s formula :  

Area of the ∆ , A = √s (s - a) (s - b) (s - c)

A = √18(18 - 16)(18 - 8)(18 - 12)

A = √18 × 2 × 10 × 6

A = √(36 × 60)  

A = √36 × 15 × 4  

A = 6 × 2√15

A = 12√15

A = 12 × 3.87

A = 46.44 cm²

Hence, the area of the triangle is 46.44 cm².

Answer 2

Step-by-step explanation:

Let sides Be 4x, 2x, 3x

4x+2x+3x=36

9x=36

x=4

Sides = 4x=16

2x= 8

3x=12

Area of triangle

Apply heron formula

√s(s-a) (s-b) (s-c)

s= 36/2=18

√18(18-16)(18-8)(18-12)

√18*2*10*6

= √2160 or 12√15