Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
pyramid abcd is similar to pyramid wxyz. the perimeter of triangle bcd is 16, and the perimeter of triangle xyz is 32. what is the scale factor to dilate abcd to wxyz?
the scale factor is

Explanation:

Step1: Recall the scale - factor formula

The scale factor \(k\) of two similar figures is given by the ratio of the corresponding linear measurements. For similar pyramids (or any similar 3 - D figures), if we consider the perimeters of corresponding faces (since perimeter is a linear measurement), the formula for the scale factor \(k=\frac{\text{Perimeter of smaller figure}}{\text{Perimeter of larger figure}}\)

Step2: Identify the perimeters

Let the perimeter of \(\triangle BCD\) (from pyramid \(ABCD\)) be \(P_1 = 16\) and the perimeter of \(\triangle XYZ\) (from pyramid \(WXYZ\)) be \(P_2=32\)

Step3: Calculate the scale factor

Using the formula \(k=\frac{P_1}{P_2}\), substitute \(P_1 = 16\) and \(P_2 = 32\)

$$k=\frac{16}{32}=\frac{1}{2}$$

Answer:

\(\frac{1}{2}\)