# The Sides of a Triangle Are in the Ratio 5:12:13 and Its Perimeter is 150 M. Find the Area of the Triangle. - Mathematics

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

#### 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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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 17 Perimeter and Areas of Plane Figures
Q 4