Question

Find the unknown side length, x. Write your answer in simplest radical form.

Answer 1

Answer:

x = 5√10

Step-by-step explanation:

Check out the picture below, where I named the vertices and I'm going to refer to it in my explanation.

Side AC is 8 and side AB is 3.
Therefore:
BC = AC - AB = 8 - 3 = 5

We know only one side in triangle BCD so that's not enough information to calculate x. But we can get side CD from triangle ACD and with that side we'll have enough info to use Pythagorean Theorem in triangle BDC.

Now let's use Pythagorean theorem in the right triangle ACD to get side CD.

Pythagorean Theorem:
$\text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2$

Hypotenuse in triangle ACD is AD.

$\text{AD}^2 = \text{AC}^2 + \text{CD}^2\\17^2 =8^2 + \text{CD}^2\\17^2 - 8^2 = \text{CD}^2\\\text{CD}^2 = 225\\CD = 15$

Now that we have side CD, we can use Pythagorean Theorem again in triangle BCD to get x! Hypotenuse in triangle BCD is x.

$x^2 = \text{BC}^2 + \text{CD}^2\\x^2 = 5^2 + 15^2\\x^2 = 250\\x = \sqrt{250}\\x = 5\sqrt{10}$