Questions: Suppose WZ=15 and WX=17. What does Y̅YX equal? Y̅X=

Transcript text: Suppose $W Z=15$ and $W X=17$. What does $\bar{Y} Y X$ equal? \[ { }^{-} Y X= \]

Solution

Solution Steps

Step 1: Identify the type of triangle

Triangle WZX is a right triangle because angle WZX is 90 degrees. Also, segment WZ is perpendicular to segment ZX.

Step 2: Use the Pythagorean theorem

Since triangle WZX is a right triangle, we can use the Pythagorean theorem: $WZ^2 + ZX^2 = WX^2$. We are given that WZ = 15 and WX = 17. Substituting these values into the equation, we get $15^2 + ZX^2 = 17^2$, which simplifies to $225 + ZX^2 = 289$.

Step 3: Solve for ZX

Subtracting 225 from both sides gives $ZX^2 = 64$. Taking the square root of both sides gives ZX = 8.

Step 4: Find YX

Since WZ is perpendicular to ZX, and YZ is part of ZX, WZ is also perpendicular to YZ. Thus, triangles WZY and WZX are both right triangles. The question says that line segment WZ bisects XY, so we know that XY is divided in half. This means that YZ and ZX are congruent, so YZ and ZX are equal in length. Since ZX=8, YZ=8 as well. Therefore, YX=YZ+ZX = 8+8 = 16.

Final Answer

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