Answer:
x = 26, y = 19
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{ST}{NP}[/tex] = [tex]\frac{RS}{MN}[/tex] , substitute values
[tex]\frac{x}{13}[/tex] = [tex]\frac{32}{16}[/tex] = 2 ( multiply both sides by 13 )
x = 26
and
[tex]\frac{MP}{RT}[/tex] = [tex]\frac{MN}{RS}[/tex] , substitute values
[tex]\frac{y}{38}[/tex] = [tex]\frac{16}{32}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 38 ( divide both sides by 2 )
y = 19
