Alright, let's work through the problem step by step!
Given:
- A triangle was dilated by a scale factor of 2.
- [tex]$\overline{ FD }$[/tex] measures 6 units.
- We need to find the length of [tex]$\overline{ DE }$[/tex] given the choice options: 3.6 units, 8 units, 10 units, 12.4 units.
However, there was no mention in the question about [tex]$\cos a^{\circ}$[/tex] (which seems to be irrelevant to our calculations). The key detail we need to focus on is the dilation and the length of [tex]$\overline{ FD }$[/tex] being mentioned.
Step 1: First, consider the original length of [tex]$\overline{ DE }$[/tex] before dilation, which is stated to be 3.6 units.
Step 2: Since the triangle is dilated by a scale factor of 2, we need to find the length of [tex]$\overline{ DE }$[/tex] after this dilation.
The rule of dilation says that the new length after dilation can be found by multiplying the original length by the scale factor.
Step 3: We multiply the original length of [tex]$\overline{ DE }$[/tex] by the scale factor 2.
[tex]\[ \overline{DE\text{ (new)}} = \overline{DE\text{ (original)}} \times \text{scale factor} \][/tex]
[tex]\[ \overline{DE\text{ (new)}} = 3.6 \times 2 \][/tex]
Step 4: Perform the multiplication:
[tex]\[ \overline{DE\text{ (new)}} = 7.2 \][/tex]
That gives us the length of [tex]$\overline{ DE }$[/tex] after the dilation, which is 7.2 units.
So, the correct answer from the given options is:
None of the provided options match 7.2 units. None of the given options (3.6 units, 8 units, 10 units, 12.4 units) are correct.
In conclusion, [tex]$\overline{ DE }$[/tex] after dilation is 7.2 units.
