Answered

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what is the area of xyz

Sagot :

Triangle MNP is similar to triangle XYZ, so ratio of corresponding are equal.

[tex]\frac{MN}{XY}=\frac{NP}{YZ}[/tex]

Subtitute the length of sides in the equation to determine the side XY.

[tex]\begin{gathered} \frac{16}{XY}=\frac{12}{3} \\ XY=\frac{16}{4} \\ XY=4 \end{gathered}[/tex]

Determine the area of triangle XYZ.

[tex]\begin{gathered} A=\frac{1}{2}\cdot XY\cdot YZ \\ =\frac{1}{2}\cdot4\cdot3 \\ =\frac{12}{2} \\ =6 \end{gathered}[/tex]

So area of triangle XYZ is 6 square units.

Option A is correct answer.

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