Question

Zу412Which of the following represents the values of x, y, and z?

Answer 1

The figure for the triangle is,

Consider the triangle ABC and triangle ABD.

`\begin{gathered} \angle ABD=\angle\text{ABC (Common angle)} \\ \angle ADB=\angle BAC\text{ (Each angle 90 degr}e\text{)} \\ \Delta ABD\cong\Delta CBA \end{gathered}`

So ratio of corresponding side is equal.

`(AB)/(CB)=(BD)/(BA)=(AD)/(CA)`

Determine the measure of side AB by using the sides ratio.

`\begin{gathered} (AB)/(12)=(12-4)/(BA) \\ (BA)^2=12\cdot8 \\ (x)^2=96 \\ x=\sqrt[]{96} \\ =4\sqrt[]{6} \end{gathered}`

Determine the measure of side y.

`\begin{gathered} y^2=x^2-(8)^2 \\ =96-64 \\ =32 \\ y=\sqrt[]{32} \\ =4\sqrt[]{2} \end{gathered}`

Determine the mesure of side z.

`\begin{gathered} z^2=y^2+(4)^2 \\ =32+16 \\ z=\sqrt[]{48} \\ =4\sqrt[]{3} \end{gathered}`

Thus option B is correct.