Question

An architect planned to construct two similar stone pyramid structures in a park. The

figure below shows the front view of the pyramids in her plan, but there is an error in
the dimensions:
7.5 ft
6 ft
2.5 ft
3 ft
B
R
10.5 ft
3.5 ft
Which of the following changes should she make to the length of side AB to correct
her error? (6 points)
1) Change the length of side AB to 2 feet
2) Change the length of side AB to 8 feet
3) Change the length of side AB to 1 foot
4) Change the length of side AB to 4 feet

Answer 1

1. Change the length of side AB to 2 feet

Explanation:

Since both stone pyramid structures are to be similar, the ratio of their corresponding side lengths must be equal. That is:

`(PR)/(AC) = (PQ)/(AB) = (RQ)/(CB)`

Since it is said there was an error in side AB, let's assume AB is unknown.

Use the following to find the length of side AB that would be used if she is to make the correction:

`(PR)/(AC) = (PQ)/(AB)`

PR = 7.5

AC = 2.5

PQ = 6

AB = x

Plug in the values

`(7.5)/(2.5) = (6)/(x)`

Cross multiply

`7.5*x = 6*2.5`

`7.5x = 15`

Divide both sides by 7.5

`x = (15)/(7.5)`

`x = 2`

AB = x = 2

Therefore, she should change the length of side AB to 2 feet.