Question

1. these two triangles are similar.

a.) find the length of side x.
b.) describe a sequence of transformations to take the small triangle to the large triangle.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{9}{x}=\frac{6}{24}\).

Step2: Solve for \(x\)

Cross - multiply: \(6x = 9\times24\). Then \(6x=216\). Divide both sides by 6: \(x=\frac{216}{6}\).

For part b, since the ratio of side lengths is \(24\div6 = 4\) (scale factor). A sequence of transformations could be a dilation (enlargement) with a scale factor of 4 centered at a point (any point, for simplicity, we can assume the center of dilation is the vertex of the triangle).

Answer:

a. \(x = 36\)