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 CB to correct her error?
Change the length of side CB to 13 feet
Change the length of side CB to 11 feet
Change the length of side CB to 8 feet
Change the length of side CB to 8.5 feet

Answer 1

The correct answer is C

Answer 2

Answer:

The correct option is C) Change the length of side CB to 8 feet.

Step-by-step explanation:

Consider the provided figures.

It is given that the pyramids are similar.

In triangle PQR and ABC, it is given that:

$\angle{P}=\angle{A}$

$\angle{Q}=\angle{B}$

By AA rule of similarity,

$\triangle{PQR}=\triangle{ABC}$

The corresponding sides of similar triangles are proportional.

$\frac{PR}{AC}=\frac{PQ}{AB}=\frac{RQ}{CB}$

$\frac{PR}{AC}=\frac{7.5}{6}=1.25$

$\frac{PQ}{AB}=\frac{5}{4}=1.25$

$\frac{RQ}{CB}=\frac{10}{9}=1.111$

$\frac{PR}{AC}=\frac{PQ}{AB}\neq{\frac{RQ}{CB}}$

Therefore, there is an error in the length of CB. Let the new length of CB is x.

$\frac{PQ}{AB}=\frac{RQ}{CB}$

$\frac{5}{4}=\frac{10}{x}$

Multiply both sides by x.

$\frac{5\times x}{4}=10$

Multiply both sides by 4.

$5x=40$

Divide both sides by 5.

$x=8$

Therefore the length of CB must be 8 feet.

Hence, the correct option is C) Change the length of side CB to 8 feet.