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,
[tex]\angle P=\angle A[/tex] (Given)
[tex]\angle Q=\angle B[/tex] (Given)
By AA rule of similarity,
[tex]\triangle PQR=\triangle ABC[/tex]
The corresponding sides of similar triangles are proportional.
[tex]\frac{PQ}{AB}=\frac{RQ}{CB}=\frac{PR}{AC}[/tex]
[tex]\frac{PQ}{AB}=\frac{6}{4}=1.5[/tex]
[tex]\frac{RQ}{CB}=\frac{9.5}{7}=1.35714285714[/tex]
[tex]\frac{PQ}{AB}neq \frac{RQ}{CB}[/tex]
It means there is an error in the dimensions. Let the new length of RQ be x.
[tex]\frac{PQ}{AB}=\frac{RQ}{CB}[/tex]
[tex]\frac{6}{4}=\frac{x}{7}[/tex]
Multiply both sides by 7.
[tex]\frac{6\times 7}{4}=x[/tex]
[tex]\frac{42}{4}=x[/tex]
[tex]10.50=x[/tex]
Therefore the length of RQ must be 10.50. The correct option is 2.
