Question

In the figure above what is the value of X what is the measure is side WZ

Answer 1

Based on the diagram, we have two right triangles. These are triangle WYT and triangle WYZ.

Since both legs of each triangle is congruent to each other, we can also say that their hypotenuse are congruent too.

Thus, TW = WZ or 2x = 3x - 5.

From this, we can now solve for x.

`\begin{gathered} 2x=3x-5 \\ \text{Subtract 3x on both sides.} \\ 2x-3x=3x-3x-5 \\ -x=-5 \\ \text{Divide by -1 on both sides.} \\ x=5 \end{gathered}`

Therefore, the value of x = 5.

To solve for WZ, let's plug in x = 5 to 3x - 5.

`\begin{gathered} WZ=3x-5 \\ WZ=3(5)-5 \\ WZ=15-5 \\ WZ=10 \end{gathered}`

Therefore, WZ = 10.

To summarize, x = 5 and WZ = 10. (Option A)