Consider a, b and c as the sides of a triangle and s as the semi perimeter
So we get
s – a = 8cm
s – b = 7cm
s – c = 5cm
We know that
(s – a) + (s – b) + (s – c) = 8 + 7 + 5
On further calculation
3s – (a + b + c) = 20
We know that a + b + c = 2s
3s – 2s = 2
So we get
s = 20
By substituting the value of s
a = s – 8 = 20 – 8 = 12cm
b = s – 7 = 20 – 7 = 13cm
c = s – 5 = 20 – 5 = 15cm
Therefore, the area of the triangle is 20√14 cm2.