The area of the triangle with sides a, b, and c can be calculated in two ways:

1) \(1/2\)*b*a
2) \(1/2\)*c*h

So, \(1/2\)*b*a = \(1/2\)*c*h . ----- eq(1)

Quantity A
\(abc\)
\(abc\)
Dividing by c
ab
Dividing by 2
(1/2)(ab)

Quantity B
\(h(a^2+b^2)\)
since, \(a^2 + b^2= c^2 , h c^2 \)
hc
(1/2)(hc)


We determined these two quantities are equal in equation 1, Hence option C is correct.