We will solve this question using the similar angle theorem
The shape consist of two triangles which i am going to draw out,
One is a big triangle while the other is a small triangle
Let NZ = a
To find NZ We will equate the ratio of the big triangle to that of the small triangle
[tex]\frac{7.5\operatorname{cm}}{3\operatorname{cm}}=\frac{(a+5)cm}{5\operatorname{cm}}[/tex]We then cross multiply to get,
[tex]\begin{gathered} 3(a+5)=7.5\times5 \\ 3a+15=37.5 \\ by\text{ collecting like terms we will have that} \\ 3a=37.5-15 \\ 3a=22.5 \\ \frac{3a}{3}=\frac{22.5}{3} \\ a=7.5\operatorname{cm} \end{gathered}[/tex]Therefore XZ=XN+NZ
[tex]XZ=5+7.5=12.5\operatorname{cm}[/tex]To calculate YZ ,
We will use the pythagorean theorem,
[tex]\begin{gathered} XZ^2=YZ^2+XY^2 \\ 12.5^2=YZ^2+7.5^2 \\ 156.25=YZ^2+56.25 \\ YZ^2=156.25-56.25 \\ YZ^2=100 \\ YZ=\sqrt[]{100} \\ \vec{YZ}=10.0cm \end{gathered}[/tex]Therefore ,
The value of YZ is
[tex]\vec{YZ}=10.0\operatorname{cm}[/tex]Hence ,
The correct answer is OPTION B
