Answer:
FJ = 32
IJ = 24
FG = 48
Explanation:
Given: HGFJI ~ AEDCB
From inspection of the diagram, the corresponding sides are:
HG~AE
FG~DE
FJ~DC
IJ~CB
IH~BA
The only pair of sides that both have side lengths are IH and BA. Therefore, we can use these to figure out the scale factor of dilation.
IH = 72 and BA = 36
⇒ IH/BA= 72/36 = 2
Therefore, HGFJI is an enlargement of AEDCB by a scale factor of 2
If HG = 56
⇒ AE = 56 ÷ 2 = 28
If DE = 24
⇒ FG = 24 × 2 = 48
If DC = 16
⇒ FJ = 16 × 2 = 32
If CB = 12
⇒ IJ = 12 × 2 = 24