Find the values of x, y, and z. The diagram is not to scale 36, 18,64 .
A x = 86, y = 94, z = 75
B x = 80, y = 62, z = 100
C x = 86, y = 75, z = 82
D x = 83, y = 67, z = 104
The information provided is not sufficient to determine the values of x, y, and z.
It is not possible to determine the values of x, y, and z just based on the given information "36, 18, 64" since there is no clear relationship or equation provided. Therefore, none of the answer choices A, B, C, or D can be determined as the correct answer.
To find the values of x, y, and z, we need to analyze the relationships between the numbers in the given diagram.
The numbers given, 36, 18, and 64, represent the lengths of the sides of a triangle, but the diagram is not to scale.
One way to determine the values of x, y, and z is to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Let's calculate the values for each option:
Option A: x = 86, y = 94, z = 75
Using the Pythagorean theorem:
x^2 = y^2 + z^2
86^2 = 94^2 + 75^2
7396 = 8836 + 5625
This equation is not true, so option A is not correct.
Option B: x = 80, y = 62, z = 100
Using the Pythagorean theorem:
x^2 = y^2 + z^2
80^2 = 62^2 + 100^2
6400 = 3844 + 10000
This equation is not true, so option B is not correct.
Option C: x = 86, y = 75, z = 82
Using the Pythagorean theorem:
x^2 = y^2 + z^2
86^2 = 75^2 + 82^2
7396 = 5625 + 6724
This equation is true, so option C satisfies the conditions.
Option D: x = 83, y = 67, z = 104
Using the Pythagorean theorem:
x^2 = y^2 + z^2
83^2 = 67^2 + 104^2
6889 = 4489 + 10816
This equation is not true, so option D is not correct.
Therefore, the correct answer is C: x = 86, y = 75, z = 82.