Given that bd is the length of the mid-segment. what is the length of ae?

The length of AE is 8 units .

Step-by-step explanation:

Now by using the midpoint theorem .

This theorem states that the segment joining two sides of a triangle at the midpoints  is parallel to the third side and is half the length of the third side .

Thus

BD is the segment joining midpoints B and D of triangle and is parallel to side AE.

BD = 4 units

Putting in the above

AE = 4 × 2

AE = 8 units

Therefore the length of AE is 8 units .

2nd one in the first row is correct

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have