Question

8. The medians of a right triangle which are drawn from the vertices of the acute angles are 5 cm and 2√10
Determine its hypotenuse.​

Answer 1

Answer:

In △ABC,

AE and CD are the medians of the triangle.

So, AE=6 and CD=8

Hence, BE=EC=21BC and AD=DB=21AB

In △ABE

AE2=AB2+BE2

∴36=AB2+41BC2           ....(1)

In △BCD

CD2=DB2+BC2

∴64=41AB2+BC2           ....(2)

Adding (1) and (2), we get

100=45(AB2+BC2)

∴AC2=80

∴AC=45 cm



Step-by-step explanation:

Hope's it helps you