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:
Two similar scalene triangles PQR and ABC with angle P congruent to angle A, angle Q congruent to angle B, and QR and BC as the bases of the triangles. The length of PQ is 6 feet, the length of QR is 9.5 feet, and the length of RP is 7.5 feet. The length of AB is 4 feet, the length of BC is 7 feet, and the length of CA is 5 feet.

Which of the following changes should she make to the length of side RQ to correct her error?

Change the length of side RQ to 9 feet
Change the length of side RQ to 10.5 feet
Change the length of side RQ to 8 feet
Change the length of side RQ to 11.5 feet

Answer 1

The correct answer is 10.5 feet because I did the same problem by I had to find ca side my given was that RQ is 10.5

Answer 2

Answer:

The correct option is 2. She can change the length of side RQ to 10.5 feet to correct her error.

Step-by-step explanation:

In triangle PQR and ABC,

$\angle P=\angle A$                       (Given)

$\angle Q=\angle B$                       (Given)

By AA rule of similarity,

$\triangle PQR=\triangle ABC$

The corresponding sides of similar triangles are proportional.

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

$\frac{PQ}{AB}=\frac{6}{4}=1.5$

$\frac{RQ}{CB}=\frac{9.5}{7}=1.35714285714$

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

It means there is an error in the dimensions. Let the new length of RQ be x.

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

$\frac{6}{4}=\frac{x}{7}$

Multiply both sides by 7.

$\frac{6\times 7}{4}=x$

$\frac{42}{4}=x$

$10.50=x$

Therefore the length of RQ must be 10.50. The correct option is 2.