Question

The Pyramid of Khufu in Giza, Egypt was the world’s 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 the center of dilation.

The cross section is at a height of 96 meters.



What are the dimensions of the cross section?

Answer 1

A height of 96 meters, the base of the cross-section is approximately 154 meters.

To find the dimensions of the cross-section at a height of 96 meters, you can use similar triangles formed by the original pyramid and the dilated cross-section.

Given:

Original height of the pyramid = 144 meters

Base length of the pyramid = 231 meters

Height of the cross-section = 96 meters

First, let's find the ratio of the height of the cross-section to the original height of the pyramid:

`Ratio=(Height of cross-section)/(Original height)=(96)/(144)=(2)/(3)`

Now, since the cross-section is a dilation of the base at a certain height, the ratio of the corresponding sides of the pyramid and the cross-section will be the same.

The base length of the cross-section can be found using this ratio:

Base length of cross-section=
`(2)/(3)`×Base length of pyramid

Base length of cross-section=
`(2)/(3)` ×231meters=154meters

Therefore, at a height of 96 meters, the base of the cross-section is approximately 154 meters.