Answer: Option C
Step-by-step explanation:
The fact that the trapezoid EFGH and the trapezoid ABCD are similar, this means that any dimension must be scaled by the same scale factor.
so:
AB = a*HG
DC = a*EF
H1 = a*H2
where a is the scale factor.
so we have that:
15cm = a*GH
9cm = a*EF
3cm = a*H2
now, let's analyze the options:
A) if EF = 27cm, we have:
9cm = a*27cm
a = 9/27 = 1/3
GH = 45cm
15cm = a*45cm
a = 15/45 = 1/3
and H2 = 3cm
3cm = a*3cm
a = 1
The scale factor is not the same in the 3 equations, so this option is not correct.
B) here we have that GH = 15cm = AB, so from this we will have a = 1, but the heights are different, so this can not be the correct option.
C) EF = 18cm
9cm = a*18cm
a = 1/2
GH = 30cm
15cm = a*30cm
a = 1/2
H2 = 6cm
3cm = a*6cm
a = 1/2
in this case we have that a is the same for the 3 equation, so the scale factor is constant and we have that bot trapezoids are similar.
Option D also has different scale factors, where for the lines EF and GH the scale factor is a = 1/4, and for the height the scale factor is 1/3.
The only correct option is C.
