PLEASE HELP I WILL GIVE 100 POINTS!!!!!!!!Given rectangle ABCD ~ HGFE , what is the length of HG ?Enter your answer in the box.length of HG =

Since rectangle ABCD is similar to  HGFE, the ratios of the lengths of their corresponding sides are equal. We can infer form our picture that AD is corresponding to EH and DC is corresponding to HG, so lets find the ratios of those corresponding sides and establish a proportion to find the length of HG:
[tex] \frac{AD}{EH} = \frac{DC}{HG} [/tex]
We know that [tex] AD=45[/tex], [tex]EH=27[/tex], and [tex]DC=15[/tex], so lets replace those values in our proportion:
[tex] \frac{45}{27} = \frac{15}{HG} [/tex]
[tex]HG= \frac{27*15}{45} [/tex]
[tex]HG= \frac{405}{45} [/tex]
[tex]HG=9[/tex]

We can conclude that the length of the segment HG is 9.