Question

due on 11.03.2025 10 total points 2 total attempts answer the question correctly to continue! a triangle is dilated. the original triangle has sides 5, 12, 13 and the dilation has sides 10, y, 26. what is the value of y?

Explanation:

Step1: Find the scale factor

The scale factor \( k \) is found by comparing corresponding sides. The original side \( 5 \) and the dilated side \( 10 \). So, \( k=\frac{10}{5} = 2\).

Step2: Calculate \( y \)

Since the sides of similar triangles (after dilation, the triangles are similar) are in proportion. The original side \( 12 \) corresponds to \( y \). Using the scale factor \( k = 2\), we have \( y=12\times k\). Substitute \( k = 2\) into the equation: \( y = 12\times2=24\).

Answer:

\(24\)