Question

6. The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter 150 m. Find the area of the triangle. ​

Answer 1

750 m²

Step-by-step explanation:

Let us consume the first side of the triangle be = 5x

Second side of the triangle be = 12x

Third Side of the triangle be = 13x

Now, Perimeter is = 150 m.

So, Perimeter of a Triangle = Sum of all sides

⇒150 m = 5x + 12x + 13x

⇒150 m = 30x

⇒x = 150/30

⇒X = 5 m

We got the value of x that is 5m, So now we will put the value of x in First side of the triangle.

1st side = 5 x 5 = 25m [Side a]

2nd side = 12 x 5 = 60m [Side b]

3rd side = 13 x 5 = 65m [Side c]

Now, We have to find the Area of the triangle

We can find the Area of the triangle by Heron's Formula:

⇒√s(s - a) (s - b) (s - c)

Value of S = a + b + c / 2

⇒S = 25 + 60 + 65 / 2

⇒S = 160 / 2

⇒S = 75 m

⇒√s (s - a) (s - b) (s - c)

⇒√75 (75 - 25) (75 - 60) (75 - 65)

⇒√75 x 50 x 15 x 10

⇒√15 x 5 x 5 x 10 x 15 x 10

⇒15 x 5 x 10

⇒ 750

⇒ 750 m²