Question

triangle efg is dilated by a scale factor of 6 to form triangle efg. side ge measures 66. what is the measure of side ge?

Explanation:

Step1: Recall dilation property

Dilation scales a figure by a scale factor. If a figure is dilated by scale factor \( k \), the length of a side of the image is \( k \) times the length of the corresponding side of the original figure. Here, scale factor \( k = 6 \), and the length of \( G'E' \) (image side) is 66. Let the length of \( GE \) (original side) be \( x \). Then \( G'E'=k\times GE \), so \( 66 = 6\times x \).

Step2: Solve for \( x \)

To find \( x \), divide both sides of the equation \( 66 = 6x \) by 6. So \( x=\frac{66}{6}=11 \).

Answer:

11