Answer:
Option D is correct.
Length of PQ is 36 unit.
Explanation:
If the measures of two sides in one triangle are proportional to the corresponding sides in the another triangle and their including angles are congruent, then the triangles are similar.
Given: Right angle triangle ABC at B , Length of AB = 12 unit and length of BC = 11.5 unit and in right angle triangle PQR at Q , length of QR = 34.5 unit.
Also it is given that  Angle A is congruent to angle P and angle C is congruent to angle R.
To find the length of QR:
It is given that ΔABC and ΔPQR are Similar triangle
then, by the definition of similar triangle:
[tex]\frac{PQ}{AB} = \frac{QR}{BC}[/tex]
Substitute the value of AB, QR and BC to solve for PQ;
[tex]\frac{PQ}{12}=\frac{34.5}{11.5}[/tex] or
[tex]PQ = \frac{34.5 \times 12}{11.5}[/tex]
On simplify:
[tex]PQ = 3 \times 12 = 36[/tex]
Therefore, the length of side PQ is 36 units.
