Sabrina is ordering a custom circular glass table for her dining room the tables are ordered based on the area of the table top
1 answer:
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Answer:
Step-by-step explanation:
We can use the properties of some of these circles to solve and find the value of x.
FIrst off - we know that to find the side of a right triangle we can use the Pythagorean Theorem, which states that (a and b being legs, c being the hypotenuse.)
We also know that this triangle is in a circle. Part of the hypotenuse and the altitude of the triangle are in the circle.
Point W is the center of the circle. Therefore, any points stretching to the edge from it will be equal (since this is a circle).
With this knowledge - UW and WZ are equal.
Therefore, since UW is , WZ will be too.
We also know the length of VZ. We can add this to WZ to find the length of the whole hypotenuse.
So the length of the hypotenuse, WV, is .
Now that we know the length of the hypotenuse, we can use the Pythagorean Theorem like we stated before to find the value of x.
We know the two legs are and
, while the hypotenuse is
(use FOIL to find the value of each expression squared)
(simplify the left side)
(subtract both sides by
)
(Quadratic formula)
(plug in values from equation)
(simplify)
(simplify)
(simplify)
(use plus/minus to find two roots)
(simplify)
1 can not be a possible answer because UW would end up being units long! This isn't possible!
Therefore, the correct answer would be B) 4.
Hope this helped!