Sides of a triangle are in the ratio of 5:12:13 and it's perimeter is

1.	Sides of a triangle are in the ratio of 5:12:13 and it's perimeter is 150m. find its area
Answer» 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.

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

Answer»

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.