\begin{tabular}{l} Drag and drop the correct answers to fill in the blanks. \ Sam made a design with two similar triangles in such a way that the \ smaller triangle Is inside the larger triangle. \ The larger triangle is made by dilating the smaller triangle. \ If the scale factor is 2 , then the side measures of the smaller triangle \ are: \ $$ A B= $$ \ $$ B C= $$ \ $$ A C= $$ \ \hline 3 cm \ \hline 5 cm \ \hline\end{tabular}

Question

UpStudy AI · Accepted Answer

To solve the problem, we need to understand the relationship between the side lengths of the smaller triangle and the larger triangle when a dilation is applied.

1. **Understanding Dilation**: 
   - Dilation is a transformation that alters the size of a figure but maintains its shape. The scale factor indicates how much larger or smaller the figure becomes.
   - In this case, the scale factor is 2, meaning that each side of the larger triangle is twice the length of the corresponding side of the smaller triangle.

2. **Finding the Side Lengths of the Smaller Triangle**:
   - Let the side lengths of the smaller triangle be denoted as:
     - $$ AB = x $$
     - $$ BC = y $$
     - $$ AC = z $$

- Since the larger triangle is formed by dilating the smaller triangle with a scale factor of 2, we can express the side lengths of the larger triangle as:
     - $$ AB_{large} = 2x $$
     - $$ BC_{large} = 2y $$
     - $$ AC_{large} = 2z $$

3. **Given Side Lengths**:
   - The problem provides the following possible side lengths for the smaller triangle:
     - $$ 3 \, 	ext{cm} $$
     - $$ 5 \, 	ext{cm} $$

4. **Calculating the Corresponding Larger Triangle Side Lengths**:
   - If we assign $$ AB = 3 \, 	ext{cm} $$:
     - Then $$ AB_{large} = 2 	imes 3 = 6 \, 	ext{cm} $$
   - If we assign $$ AB = 5 \, 	ext{cm} $$:
     - Then $$ AB_{large} = 2 	imes 5 = 10 \, 	ext{cm} $$

5. **Conclusion**:
   - Since we need to fill in the blanks for the smaller triangle's side lengths, we can assign the values as follows:
     - $$ AB = 3 \, 	ext{cm} $$
     - $$ BC = 5 \, 	ext{cm} $$
     - $$ AC $$ can be any value that maintains the triangle inequality, but since we only have two values, we can assign $$ AC = 3 \, 	ext{cm} $$ or $$ 5 \, 	ext{cm} $$ as well.

Thus, the side measures of the smaller triangle can be filled in as:
- $$ AB = 3 \, 	ext{cm} $$
- $$ BC = 5 \, 	ext{cm} $$
- $$ AC = 3 \, 	ext{cm} $$ (or $$ 5 \, 	ext{cm} $$ depending on the choice).

If you need a specific assignment for $$ AC $$, please clarify!
$$ AB = 3 \, 	ext{cm} $$, $$ BC = 5 \, 	ext{cm} $$, $$ AC = 3 \, 	ext{cm} $$

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Geometry Questions