Question

the area of triangle is 150cm and it's side are in the ratio 3:4:5then find the perimeter of triangle​

Answer 1

Step-by-step explanation:

hope it will be helpful to you

Answer 2

Solution :-

Let the given ratios be 3x, 4x and 5x

Now,

It is given that,

Area of triangle is 150cm

Therefore ,

S = 3x + 4x + 5x /2 = 12x/2 = 6x

By using Heron's Formula,

$\sqrt{6x(6x - 3x)(6x - 4x)(6x - 5x)}$

$\sqrt{6x(3x)(2x)(x) } \\ \sqrt{36 {x}^{4} } \\ = 6 {x}^{2}$

Now,

6x^2 = 150

x^2 = 150/6

x^2 = 25

x = √25

x = 5

Thus, The value of x is 5

Therefore,

All sides of a given triangle are

3 * 5 = 15 cm

4 * 5 = 20 cm

5* 5 = 25 cm

Now,

As we know that,

Perimeter of triangle

= Side + side + side

= 15 + 20 + 25

= 35 + 25

= 60

Hence, The perimeter of the given triangle is 60cm $.$