Question

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

Answer 1

Let the sides of a triangle be `5xm,12xm and 13xm` 

Since, perimeter is the sum of all the sides, 

`5x+12x+13x=150` 

⇒` 30x=150` 

Or, `x=150/30=5` 

The lengths of the sides are: 

`a=5xx5=25m` 

`b=12xx5=60m` 

`c=13xx5=65 m` 

Semi-perimeter (s) of the triangle = `"perimeter"/2=(25=60+65)/2=150/2=75m` 

Area of triangle= `sqrt(s(s-a)(s-b)(s-c))` 

=`sqrt(75(75-25)(75-60)(75-65))` 

=`sqrt(75xx50xx15xx10)` 

=`sqrt(562500)` 

=`750m^2`