Question

Which measurements would be correct for trapezoid EFGH if it were similar to trapezoids ABCD?

A side EF=27 cm; side GH = 45 ; height = 3 cm
B side EF=18 cm; side GH = 15 ; height = 6 cm
C side EF=18 cm; side GH = 30 ; height = 6 cm
D side EF=36 cm; side GH = 60 ; height = 9 cm

Answer 1

C side EF=18 cm; side GH = 30 ; height = 6 cm

Answer 2

Answer: Option C

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.