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

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#### Solution

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`

Concept: Areas of Combinations of Plane Figures

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