Question

side of triangle are in the ratio of 4:2:3 and it's perimeters is 36 cm. find its area.

Answer 1

Answer:

6 √ 30 cm²

Step-by-step explanation:

Let the side of triangle be 4x, 2x and 3x respectively.

Perimeter = 36 cm

⇒ 4x + 2x + 3x = 36

⇒ 9x = 36

⇒ x = 36 / 9

⇒ x = 4

Now, the side of triangle are;

➾ 4x = 4 * 4 = 16

➾ 2x = 2 * 4 = 8

➾ 3x = 3 * 4 = 12

To find area of triangle ;

S = $\frac{\sf Perimeter}{2}$

S = 36 / 2

S = 18

Area of Δ = $\sqrt{s(s-a)(s-b)(s-c)}$

⇒ $\sqrt{18(18-16)(18-8)(18-12)}$

⇒ $\sqrt{2 * 3 * 3 * 2 * 5 * 2 * 3}$

⇒ 2 * 3 $\sqrt{2*3*5}$

⇒ 6 $\sqrt{30}$

Hence, the area of triangle is $\bf 6\sqrt{30}\: cm^{2}$

Answer 2

Step-by-step explanation:

4x+2x+3x = 36

9x = 36

x = 4

4x = 16

2x = 8

3x =12

16+12+8/2 = 18

√18(18-16)(18-8)(18-12)

√18(2)(10)(6)

√2×9×2×2×5×2×3

√2×2×3√5×3

12√15