Right triangle, median to the hypotenuse 6, find the hypotenuse

Step by step

The question

Question: in a right triangle the median to the hypotenuse is 6: find the hypotenuse B C.

1 Use the semicircle rule

The right angle is at A.

The median A M goes to M, the middle of the hypotenuse B C.

Draw the circle with B C as its diameter.

The angle in a semicircle is 90°, so A is on this circle too.

M is the center.

M A, M B and M C are all radii: all the same length.

2 Double the median

The diameter is twice the radius: 12.

Careful!

This works for the median to the hypotenuse of a right triangle.

Not for any median.

3 Check

Let's check: M B and M C are 6 each, and together they make B C, 12.

So it is right!

Let's look back.

First: use the semicircle rule.

Then: double the median.

Last: check.