Answer:
x= [tex]10\frac{10}{7}[/tex] and y= 10.
Step-by-step explanation:
It is given that the triangles are similar.
So, the ratio of their sides will be equal.
i.e. [tex]\frac{21}{14}=\frac{16}{x}=\frac{15}{y}[/tex]
i.e. [tex]\frac{3}{2}=\frac{16}{x}=\frac{15}{y}[/tex]
This gives us that,
[tex]\frac{3}{2}=\frac{16}{x}[/tex] and [tex]\frac{3}{2}=\frac{15}{y}[/tex]
i.e. [tex]x=\frac{16\times 2}{3}[/tex] and [tex]y=\frac{15\times 2}{3}[/tex]
i.e. [tex]x=\frac{32}{3}[/tex] and [tex]y=\frac{30}{3}[/tex]
i.e. x= 10.7= [tex]10\frac{10}{7}[/tex] and y= 10
Thus, the side lengths are x= [tex]10\frac{10}{7}[/tex] and y= 10.
