Posted by **Me too** on Tuesday, March 8, 2011 at 8:43pm.

The medians of the legs of a right triangle are 3 square root 6 and 6. What is the length of the hypotenuse?

- geometry -
**tchrwill**, Wednesday, March 9, 2011 at 11:13am
Here is the same problem with different numbers.

The medians of a right triangle which are drawn from the vertices of the acute angles are 5 and root 40. What is the length of the hypotenuse? Can someone show me how to do it? thanks

Draw triangle ABC where A is the upper left vertex, B is the lower right vertex and C is the right angle at the lower left. Call AC x and BC y. Draw the medians BD and AE, D being the midpoint of x and E the midpoint of y.

From triangle ACE, x^2 + (y/2)^2 = 25 or 4x^2 + y^2 -100 = 0.---(1)

From triangle DCB, (x/2)^2 + y^2 = 40 or x^2 + 4y^2 - 160 = 0.---(2). (2)

From (1), y^2 = 100 - 4x^2

Substituting into (2) yields x = 4 and y = 6.

Therefore, the hypotenuse is sqrt(4^2 + 6^2 = 7.211.

## Answer this Question

## Related Questions

geometry - The medians of a right triangle which are drawn from the vertices of ...

Math - 1) The hypotenuse of an isosceles right triangle is 8 cm longer than ...

math - I have 14 questions and I was wondering if someone could check my answers...

Math Help!!! - please check my answers 1. Find the length of the hypotenuse of a...

math - The area of a triangle whose legs are in the ratio of 2:3 is 48. The ...

geometry - a right triangle has legs of length 3x and 4x and hypotenuse of ...

math/geometry - complete the statements: To find the length of the hypotenuse of...

Math - If the hypotenuse of a right triangle is 13 and one of its legs is 5, ...

Algebra - What is the length of the hypotenuse of a right triangle with legs of ...

Geometry - The length of a hypotenuse of a right triangle is 29 feet. The ...