Question

∆
ABC is right angled at B. AD and CE are two medians drawn from A and C. If AC = 5cm
and AD
=
3root5/2
cm. Find the length of CE

Answer 1

Answer:

2 root 5 /3

Step-by-step explanation:

We apply Pythagoras theorem.

ΔABC:  AC² = AB² + BC² 

             5² = (2 BE)² + BC²

             25 = 4 BE² + BC²    -- (1)

Also,  BE² + BC² = CE²      ----(2)

ΔABD,  AD² = AB² + BD²

                    = 4 BE² + BC²/4

=>   4 (3√5/2)² = 45 = 16 BE² + BC²  -- (3)

Solve the equations (1) and (2).

          55 = 3 BC²    => BC = √(55/3)

=>  BE² = (AC² - BC²)/4 = (5² - 55/3)/4 = 5/3

By (2), CE² = 5/3 + 55/3 = 20/3

=>   CE = 2 √(5/3)