Question

Abc is a right triangle, right angled at



b. Ad and ce are two medians drawn from a and c respectively. If ac = 5cm and ad=3√5/2cm, find the length of ce.

Answer 1

Answer:

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)

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