In the given diagram, △ ABC ~ △ PQR and AD/PS = 3/8 . The value of AB : PQ is : 1. 8 : 3 2. 3 : 5 3. 3 : 8 4. 5 : 8

Mathematics

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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.

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

∴ AB : PQ = 3 : 8.

Hence, Option 3 is the correct option.

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