Question

8 practice 8 (from unit 5, lesson 3)

the pyramid of khufu in giza, egypt, was the worlds tallest free-standing structure for more than 3,500 years. its original height was about 144 meters. its base is approximately a square with a side length of 231 meters.
the diagram shows a cross-section created by dilating the base using the top of the pyramid as a center. the cross-section has a side length of 154 meters.

a. what scale factor was used to create the cross-section?
type your answer in the box.

b. what is the height of the cross-section?
type your answer in the box.
meters

Explanation:

Step1: Calculate scale factor

The scale factor is the ratio of the cross-section side length to the base side length.
$\text{Scale factor} = \frac{154}{231} = \frac{2}{3}$

Step2: Find height of cross-section

Multiply the original pyramid height by the scale factor.
$\text{Height of cross-section} = 144 \times \frac{2}{3} = 96$

Answer:

a. $\frac{2}{3}$
b. 96 meters