Question

Find the value of x.
Answer options:
X=8
X=10
X=16
X=20

Answer 1

X = 20

Explanation:

To find the value of x you must go in a round about way to find the answer. A helpful metric would be the radius. The radius will be the same no matter what point of the circle you draw to, as long as you start in the center.

At the top we can see that there is a line marked as 10 and another sprouting from that labelled as 8. From there you can find the radius by using the Pythagorean theorem:
`\sqrt{a^(2) +b^(2) } = c`

In this case our a will be 10 and our b will be 8. Our c is is the radius.

`\sqrt{a^(2) +b^(2) } = c`

`\sqrt{10^(2) +8^(2) } = c`

`√(100 +64 ) = c`

`√(164) = c`

`2√(41) = c`

Since this is the radius the same applies to the right angle down towards the bottom. If we know that the radius is
`2√(41)` then we do not have to solve it again. Since the radius and one of the legs is the same as the other equation, that means the other leg also has to match meaning it is 10. Since that is only half of the line, we multiply it by 2 to get 20.