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Question

In the given figure, ΔABC is a right triangle right angled at B. AD and CE are the two medians drawn from A and C respectivley. If AC =5 cm and AD =352 cm, then CE =??


A

4 cm

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B

25cm

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C

35cm

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D

5 cm

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Solution

The correct option is B

25cm


Let AE =BE = a cm

and BD=DC = b cm

Using mid point theorem DE=12AC=52cm

In ΔDBE,DB2+BE2=ED2

a2+b2=254(I)

In ΔABD,AB2+BD2=AD2

(2a)2+b2=(352)2

4a2+b2=454(II)

Solving (I) and (II), we get, a2=53 and b2=5512

Now, in ΔBEC,

BE2+BC2=EC2

or,EC2=a2+(2b)2
=a2+4b2
=53+553
=603=20

EC=20 cm=25 cm


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