Question

In the given figure △ABC is a right-angle at B. AD and CE are the two medians drawn from A and C respectively. If AC = 5 cm and AD = \(\frac{3\sqrt 5}2\) cm, then CE equals 

(a) 2 cm

(b) 2√5 cm

(c) 5√2 cm

(d) 3√2 cm

Answer 1

Correct option is (b) 2√5 cm

ABC is a right angled triangle, with right angle at 90^∘

In △ABD,

Using Pythagoras theorem

AB² + BD² = AD²

4AB² + BC² = 4AD² ....... (1)

In △BEC,

Using Pythagoras theorem

BE² + BC² = CE² 

4BC² + AB² = 4CE² ........ (2)

Adding (1) and (2), we get

5AB² + 5BC² = 4(AD² + CE²)

5AC² = 4(AD² + CE²)   .....(Using Pythagoras theorem in triangle ABC)

125 = 45 + 4CE²

CE² = 20

⇒ CE = 2√5​ cm