The medians of a right triangle that are drawn from the vertices if the acute angles have lengths of 2 square root 13 and square root 73. Find the length of the hypotenuse

10 units

Step-by-step explanation:

Let a, b, c represent the sides of the right triangle, with hypotenuse c.

We are given ...

(a/2) ^2 + b^2 = (√73) ^2

a^2 + (b/2) ^2 = (2√13) ^2

Adding these two equations, we get ...

(5/4) a^2 + (5/4) b^2 = 125

Multiplying by 4/5 gives ...

a^2 + b^2 = 100

But we know that ...

a^2 + b^2 = c^2 = 100

so

c = √100 = 10

The length of the hypotenuse of the right triangle is 10.