Chapter 8: Similar Triangles

Example 16. ABC is a right triangle, right angled at C. If p is the length of the perpendicular from C to AB and a, b, c have the usual meaning, then prove that

1. pc = ab
2. 

Solution:- (i) Area of taking BC as base = 1/2 X BC X AC

= 1/2ab--------(i)

Area of taking AB as base = 1/2 X AB X CD

= 1/2 cp------(ii)

from (i) and (ii) 1/2 ab = 1/2 cp

Or, pc = ab

Or, c = ab/p---------(iii)

(ii) In right ,