In a right-angled triangle, the lengths of the medium from the vertices of acute angles are 7 cm and 4√6 cm. What is the length of the hypotenuse of the triangle (in cm)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 2√29
In right angled triangle ABC, if AD and CE are the medians then,
⇒ 4(AD2 + CE2) = 5AC2
Now, AD = 7 cm and CE = 4(6)1/2
⇒ 4 × [72 + {4(6)1/2}] = 5AC2
⇒ 5AC2 = 580
⇒ AC = 2 × (29)1/2