5. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

Suppose that the sides in cm, are 12x, 17x and 25x.

Then, we know that 12x + 17x + 25x = 540 ...(Given, Perimeter of the triangle)

54x = 540

Thus, x = 10

So, the sides of the triangle are 12 × 10cm, 17 × 10cm, 25 × 10cm i.e., 120cm, 170cm and 250cm.

Now, we know that,

Therefore,

Now, Area of triangle =

=

=

=

=

=

= 100 × 10 × 9

Therefore, area of the given triangle is 9000