Analyze the diagram below and complete the instructions that follow.

Remark
Draw a line from the left side of the 7 unit line to the side labeled x. Make sure than the new line is perpendicular to x. 

Step One
Solve for y. 
y is the hypotenuse for a 45 - 45 - 90 triangle. that means that the opposite side to the 45 degree angle (the side you just drew) and the adjacent side of the 45 degree angle are both equal to 9

So use the Pythagorean Theorem to solve for y
a^2 + b^2 = c^2
a = 9
b = 9
c = y

y^2 = 9^2 + 9^2      Pull out the common factor.
y^2 = 9^2 ( 1 + 1)   Add the 1's together.
y^2 = 9^2 (2)          Take the square root of both sides.
sqrt(y^2) = sqrt(9^2) * sqrt(2)
y = 9 * sqrt(2)

That means A is the answer if I've done this correctly.

Step Two
Find x
x = 9 + 7 = 16. Did you see where the 9 came from? Remember we  used it in step one.

7 comes from the given parallel line on top.

A is the correct answer

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