The difference between the semi-perimeter and the sides of ΔPQR are 18 cm, 17 cm and 25 cm, respectively. Find the area of the triangle.

$30\sqrt{510}cm^2$

Let the semi-perimeter be s.

The sides of a triangle = a, b, and c.

s - a = 18 --- (1)

s - b = 17 --- (2)

s - c = 25 --- (3)

Then the three sides of the triangle =
a = s - 18

b = s - 17

c = s – 25

s = \(\frac{ s – 18 + s – 17 + s - 25}{2}\) 

s = 60

Now the area of the triangle =  \(\sqrt {s(s-a)(s-b)(s-c) }\)

Now put the value of 1 , 2 and 3 in the given formula.

= \(\sqrt {60 (18)( 17)( 25) }\)  = 30\(\sqrt {510) }\)cm²