The sides of a triangle are in the ratio 8 : 9 : 10 and its perimeter is 270 cm. What is its area? 

$225\sqrt{77}cm^2$

We have,

The sides of a triangle are in the ratio 8 : 9 : 10

Its perimeter = 270 cm

so the semi perimeter will be = \(\frac{270}{2}\) = 135

According to the question,

Perimeter is the sum of all the sides of the figure.

Area of a triangle = \(\sqrt {s(s-a)(s-b)(s-c) }\)

Let the sides are = 8x , 9x and 10x

Now, 8x + 9x + 10x = 270

27x = 270

x = 10

So the sides are = 8x = 80

9x = 90

and 10x = 100

Area = \(\sqrt {135(135-80)(135-90)(135-100) }\)

= \(\sqrt {135(55)(45)(35) }\)

= $225\sqrt{77}cm^2$