∆ABC is right angled at C. 'p' is the perpendicular from C to AB; AB, BC, CA are c, a, b respectively, then:

In △ABC, where $$\angle C = 90^\circ:$$​​

AB = c (hypotenuse)

BC = a

CA = b

p is the length of the perpendicular from C to AB.

Concept Used:
In a right-angled triangle, if p is the perpendicular drawn from the right angle to the hypotenuse, the following relationship holds:

Area of right angle triangle = $$\frac{1}{2} \times base \times height$$ ​

Solution:  

From the concept of triangle;

​$$\frac{1}{2} \times b \times a = \frac{1}{2} \times p \times c \\ \ \\\bf \implies b\cdot a = p\cdot c$$​