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