To find the length of BC in similar triangles ABC and BDC, we can use the property of similar triangles where the corresponding sides are in proportion.
We have AD = 6 cm, DC = 2 cm, and LBAC = LDBC.
Using the proportionality of the corresponding sides of the similar triangles, we can set up the equation:
AB / BD = AC / DC
Let's substitute the given values:
AB / BD = AC / DC
AB / (BD + DC) = AC / DC
AB / (BD + 2) = AC / 2
Since LBAC = LDBC, we can substitute the values of AC and BD:
AB / (BD + 2) = AB / 2
Simplifying the equation, we get:
BD + 2 = 2
BD = 0
If BD = 0, triangle BDC does not exist. Therefore, there seems to be an error in the given information or the problem statement.
As for part (b), finding the area of ABDA:
Since ABDA is a parallelogram, the area can be calculated by multiplying the base (AD) by the corresponding height (BC).
Area of ABDA = AD × BC
Area of ABDA = 6 cm × BC
For part (c), to find the scale factor of the enlargement when AABC is reduced to ABDC:
The scale factor can be found by comparing the corresponding sides of the two similar triangles.
Considering the corresponding sides AB and BD:
Scale factor = AB / BD
Since BD = 0 (as discussed above), the scale factor cannot be determined.
Similarly, for the area of ABC, since we don't have the value of BC, we cannot find the area at this time.
Please double-check the given information or provide additional details if possible.