To determine the length of the side [tex]\(\overline{5}\)[/tex] of the triangle after dilation, follow these steps:
1. Understand the Given Information:
- We know [tex]\(\tan(a^\circ) = \frac{4}{3}\)[/tex], but this information isn't directly necessary for this particular calculation involving the side length.
- The original side length [tex]\(\overline{FR}\)[/tex] of the triangle is 12 units.
- The triangle was dilated by a scale factor of 4.
2. Dilation Calculation:
- The effect of dilation on a geometric figure is to multiply every side by the scale factor.
- Therefore, if the original side length [tex]\(\overline{FR} = 12\)[/tex] units, when the triangle is dilated by a scale factor of 4, the new length of [tex]\(\overline{FR}\)[/tex] becomes:
[tex]\[
\overline{FR_{\text{scaled}}} = \overline{FR} \times \text{scale factor} = 12 \times 4
\][/tex]
3. Compute the New Side Length:
- Perform the multiplication to find the new length:
[tex]\[
\overline{FR_{\text{scaled}}} = 48
\][/tex]
Thus, after the dilation by a scale factor of 4, the length of [tex]\(\overline{FR}\)[/tex] is 48 units.
