Question

The first on is the cut off answers

Answer 1

A

Explanation:

when 2 shapes are similar, then there is one common scaling factor or ratio (f) for all corresponding sides or other lengths (like heights).

so AB and DE correspond to each other in the attempted similarity relationship.

that means

1.34 × f = 2

f = 2/1.34 = 1.492537313... = 200/134 = 100/67

as mentioned, to be similar the same factor had to apply for the other pairs of corresponding sides :

DF × f = AC

DF = AC/f = 4 / 100/67 = 4×67/100 = 268/100 = 2.68

EF × f = BC

EF = BC/f = 3 / 100/67 = 3×67/100 = 201/100 = 2.01

FYI - answers B and D disqualify themselves, by making EF longer than DF (as for the corresponding "original" sides AC and BC the opposite is true).

Answer 2

A. DF 2.68 units and EF = 2.01 units

AC is 2 times longer than AB so, that must mean DF is 2 times longer than DE so, 1.34*2=2.68

DF = 2.68

Since BC is 3/2 of AB, to find EF, divide 1.34 in half and then multiply that by 3.

1.34/2 = 0.67*3 = 2.01

EF = 2.01

:)