The medium of a right triangle which are drawn from the vertices of the acute angles are 5 cm and 2√10 cm. Then
its hypotenuse is
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Step-by-step explanation:
Correct option is
C
4
5
cm
In △ABC,
AE and CD are the medians of the triangle.
So, AE=6 and CD=8
Hence, BE=EC=
2
1
BC and AD=DB=
2
1
AB
In △ABE
AE
2
=AB
2
+BE
2
∴36=AB
2
+
4
1
BC
2
....(1)
In △BCD
CD
2
=DB
2
+BC
2
∴64=
4
1
AB
2
+BC
2
....(2)
Adding (1) and (2), we get
100=
4
5
(AB
2
+BC
2
)
∴AC
2
=80
∴AC=4
5
cm
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