Question

sides of a triangle are in the ratio of 5:12:13 and it's perimeter is 150m. find its area​

Answer 1

Answer:

Area of triangle is 30m²

Answer 2

Correct question:-

Sides of a triangle are in the ratio 5:12:13 and it's perimeter is 150m. Find it's area.

Given:-

→Ratio of sides of the triangle=5:12:13

→Perimeter of the triangle=150m

To find:-

→Area of the triangle

Solution:-

Let the sides of the triangle be 5x,12x and 13x respectively.

We know that:-

→Perimeter of a triangle=Sum of 3 sides

=>5x+12x+13x= 150

=>30x = 150

=>x=150/5

=>x = 5

Thus sides of the triangle are:-

→5×5=25m

→12×5=60m

→13×5=65m

Now we will name the sides of the triangle as a,b and c respectively.

Thus, a=25m,b=60m,c=65m

Semi-perimeter of the triangle:-

=>s=150/2

=>s=75m

•(s-a)=(75-25)=50m

•(s-b)=(75-60)=15m

•(s-c)=(75-65)=10m

By Heron's formula,area of the given triangle is:-

=>∆= √s(s-a)(s-b)(s-c)

=>√75×50×15×10

=>√750×750

=> 750m²

Thus,area of the triangle is 750m².