geometry

posted by .

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

• geometry -

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.

Similar Questions

1. Math

If the hypotenuse of a right triangle is 13 and one of its legs is 5, find the area fo the triangle. Answer Choices 20 40 45 30 25 I know a hypotenuse the side of a right triangle opposite the right angle. You can't multiply the hypotenuse …
2. math/geometry

complete the statements: To find the length of the hypotenuse of a 45-45-90 triangle, multiply the length of one of the legs by:?
3. geometry

a right triangle has legs of length 3x and 4x and hypotenuse of length 75. What are the lengths of the legs of the triangle.
4. geometry

The medians of a right triangle which are drawn from the vertices of the acute angle are 5 and root 40. What is the length of the hypotenuse?
5. math

I have 14 questions and I was wondering if someone could check my answers. This is a do or die situation. If I don't get an A, I may not get to graduate. I really appreciate you taking your time to double check theses for me. Thanks …
6. Math

1) The hypotenuse of an isosceles right triangle is 8 cm longer than either of its legs. Note that an isosceles right triangle is a right triangle whose legs are the same length. Find the exact length of its legs and its hypotenuse. …
7. math

If the hypotenuse of a right triangle is 10 and one leg is 5 square root 3, then the area of the triangle is a. 5 b. 25 square root 3 c. 25 d. 50 square root 3 e. 12.5 square root 3 please answer and explain
8. math

The area of a triangle whose legs are in the ratio of 2:3 is 48. The length of the hypotenuse is a. square root 13 b. 8 c. 2 square root 52 d. 12 e. 208 please answer and explain
9. Math Help!!!

please check my answers 1. Find the length of the hypotenuse of a right triangle with the legs of 9cm and 12cm A.8 B.21 C.15 *** D.225 2.The length of a hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find the …
10. Pre-Alegrebra

1)Find the length of the hypotenuse of a right triangle with legs of 9cm and 12cm 8 cm 21 cm 15 cm**** 225 cm 2)The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is 5 cm. Find the length of the other …

More Similar Questions