To determine whether Julia's findings for the second triangle were correct, we start with analyzing the attributes of the first triangle. It has a rise of 3 and a run of 10, which gives it a slope (rise/run) of:
\[ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{3}{10} \]
For the second triangle, we know the rise is 7.5, and we want to find the correct length of the run (denote it as \( r \)) so that the triangles are similar.
Since the triangles are similar, their slopes must also be equal. Therefore, we can set up the proportion:
\[ \frac{7.5}{r} = \frac{3}{10} \]
To solve for \( r \), we can cross-multiply:
\[ 7.5 \cdot 10 = 3 \cdot r \]
This simplifies to:
\[ 75 = 3r \]
Now, divide both sides by 3:
\[ r = \frac{75}{3} = 25 \]
Therefore, for the second triangle to be similar to the first triangle, the run needs to be \( 25 \).
If Julia found a different length for the run and did not follow this proportional reasoning, she would be incorrect.
The correct choice reflecting common mistakes would be:
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
This suggests that if Julia improperly set up her proportion or made an error in comparing the triangles, she would have reached the wrong conclusion regarding the length of the run for the second triangle.
1 answer