Analyze the diagram below and complete the instructions that follow.
find the unknown side length, x. write your answer in simplest radical form.
a.
2 (square root) 41
b.
4(square root) 29
c.
48
d.
58
select the best answer from the choices provided
a
b
c
d

The correct answer option is D. 58.

Step-by-step explanation:

We are given a right angled triangle with a known side length for perpendicular and base and we are to find the value of x (hypotenuse).

For that, we will use Pythagoras Theorem.

Taking square root on both sides to get:

x = 58

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.