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In the given figure, ABC is a right triangle, right angled at B. AD and CE are the two medians drawn from A and C respectively. If $A C = 5 cm$ and $AD = 352 c m$ , find the length of CE.

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\sqrt{5}

\sqrt{5}

\sqrt{5}

\sqrt{5}

answer is B.

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Detailed Solution

It is given in the question, that ABC is a right-angled triangle and E and D are the midpoints of sides AB and BC.
It is also given that AC = 5cm.

We can observe from the figure that the given triangle is a right-angled triangle.
So, we can use the Pythagoras theorem which states that:
H²=L²+B²
For

ΔABD

A B 2 + B D 2 = A D 2 4 A B 2 + B C 2 = 4 A D 2 ...... 1

For

ΔBEC

B E 2 + B C 2 = C E 2 4 B C 2 + A B 2 = 4 C E 2 ...... 2

Add both equations

5 A B 2 + 5 B C 2 = 4 A D 2 + C E 2 5 A C 2 = 4 A D 2 + C E 2 125 = 45 + 4 C E 2

C E 2 = 20 C E = 25

The length of

C E = 25

cm .
Hence, the correct option is 2.

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