Question

In right triangle ABC, angle C = 90˚. Median AM has a length of 19, and median BN has a length of 18. What is the length of the hypotenuse of the triangle?

Answer 1

Answer:

2$\sqrt{137}$

Step-by-step explanation:

Solving for the equations,

x² + 4y² = 361

4x² + y² = 324

Add both equations

5x² + 5y² = 685

Divide both sides by 5

x² + y² = 137

Multiply both sides by 4

4x² + 4y² = 548

Now take the square of both sides.

$\sqrt{4x^{2} +4y^{2} } =\sqrt{548}$

= 2$\sqrt{137}$