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:


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:

Given that both structures are similar, it follows that the ratio of their corresponding lengths are equal.

To find out what should be the correct length of AB that she should change to, set up the proportion showing the ratio of 2 corresponding lengths of both structures. Thus:

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

We will assume AB is unknown.

PR = 7.5 ft

AC = 2.5 ft

PQ = 6 ft

Plug in the values into the equation

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

Cross multiply

`AB*7.5 = 6*2.5`

`AB*7.5 = 15`

Divide both sides by 7.5

`AB = 2`

The architect should change the length of AB to 2 ft