Question

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

Answer 1

Let the side of triangle be x.

Then AB=5x,. BC=12x and CA= 13x

Given, Perimeter(P) =150 m

But P= 5x+12x+13x = 30x

That is, 30x=150 m

Therefore,x=5m

Now AB =5x = 25m

BC= 12x =60m and CA=13x =65m

Answer 2

Let the 1st side of the triangle = 5x

the 2nd side of the triangle =12x

the 3rd side of the triangle = 13x

Then ,

According to the question,

5x + 12x + 13x = 150

30x = 150

So, x= 150/30

=5

Hence, the 1st side of the triangle = 5×5=25

the 2nd side of the triangle = 12×5=60

the 3rd side of the triangle = 13×5=65

Since, the triangle is a right triangle

= 5² +12² =13²

25+144=169

169=169

So, the Area of the triangle = 1/2×b×h

= 1/2 ×25×(60)

= 750 m²