In the given diagram, △ ABC ~ △ PQR and $\frac{AD}{PS} = \frac{3}{8}$. The value of AB : PQ is :

Given,

△ ABC ~ △ PQR

⇒ ∠B = ∠Q (Corresponding angles of similar triangle are equal)

In △ ABD and △ PQS,

⇒ ∠B = ∠Q (Proved above)

⇒ ∠D = ∠S (Both equal to 90°)

∴ △ ABD ~ △ PQS (By A.A. axiom)

We know that,

Corresponding sides of similar triangles are proportional.

$\therefore \frac{AB}{PQ} = \frac{AD}{PS} = \frac{3}{8}$.

∴ AB : PQ = 3 : 8.

Hence, Option 3 is the correct option.