These two figures are the image and pre-image of a dilation. Find the length of the missing sides.

Answer:Hence, we have:            x= 5/2 in.=2.5 in.and y+1=6 in.    ( since y=5)Step-by-step explanation:We know that if two triangles are similar then there corresponding sides are proportional.i.e. according to  the figure provided to us we have:[tex]\dfrac{4}{2}=\dfrac{5}{x}=\dfrac{y+1}{3}[/tex]On equating the first two equality we have:[tex]\dfrac{4}{2}=\dfrac{5}{x}\\\\i.e.\\\\4x=10\\\\x=\dfrac{10}{4}\\\\\\x=\dfrac{5}{2}[/tex]     Hence,   x=5/2 in.and now on equating first and third terms we have:[tex]\dfrac{4}{2}=\dfrac{y+1}{3}\\\\12=2(y+1)\\\\12=2y+2\\\\12-2=2y\\\\i.e.\\\\2y=10\\\\i.e.\\\\y=5[/tex]Hence, the length of the missing sides are:  x=5/2 in.and y+1=5+1=6 in.