Question

Medians of a right angled triangle which are drawn from the acute angles are 16 cm and 12cm respectively.
The length of hypotenuse of the triangle is

Answer 1

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

Answer 2

Medians of a right angled triangle which are drawn from the acute angles are 16 cm and 12cm respectively.

The length of hypotenuse of the triangle is_______

#shreya