Let the semi-perimeter be s

Let the sides of the triangle be a, b and c

It is given in the question that,

s – a = 8 …(i)

s – b = 7 …(ii)

s – c = 5 …(iii)

Now, by adding (i), (ii) and (iii) we get:

(s – a) + (s – b) + (s – c) = 8 + 7 + 5

3s – a – b – c = 20

3s – (a + b + c) = 20

We know that,

s =

∴ 3s – 2s = 20

s = 20 cm

Now, area of the triangle =

=

= 20 cm²

Hence, option (c) is correct