Answer:
m = [tex]\frac{16}{3}[/tex] , z = [tex]\frac{24}{5}[/tex]
Step-by-step explanation:
Δ PQT and Δ PRS are similar ( by AA postulate ), so the ratios of corresponding sides are equal, that is
[tex]\frac{PQ}{PR}[/tex] = [tex]\frac{PT}{PS}[/tex] , substitute values
[tex]\frac{m-2}{m}[/tex] = [tex]\frac{5}{8}[/tex] ( cross- multiply )
8(m - 2) = 5m ← distribute parenthesis on left side
8m - 16 = 5m ( subtract 5m from both sides )
3m - 16 = 0 ( add 16 to both sides )
3m = 16 ( divide both sides by 3 )
m = [tex]\frac{16}{3}[/tex]
and
[tex]\frac{QT}{RS}[/tex] = [tex]\frac{PT}{PS}[/tex] , substitute values
[tex]\frac{3}{z}[/tex] = [tex]\frac{5}{8}[/tex] ( cross- multiply )
5z = 24 ( divide both sides by 5 )
z = [tex]\frac{24}{5}[/tex]
