A right triangle $xYZis$ shown above where $|xY|=Z$ and $\frac{?}{{?}_x}=.$ Line segments are continually drawn $tobe$ perpendicular $to$ the triangle, $as$ shown $in$ the

figure.

$(a)$ Find the total length $of$ the perpendicular line segments $|Y_1|+|x_1{y}_1|+|x_1{y}_2|+$dots $in$ terms $ofz$ and $.$

$(b)$ Find the total length $of$ the perpendicular line segments when $z=5$ and $=\frac{}{6}.$