Given: The correspondence ABC ↔ PQR is a similarity in ∆ABC and ∆PQR.
AB = 16,
AC = 8,
PQ = 24 &
BC = 12
To find: QR + PR = ?
By definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.
To find (QR + PR), cross multiply it.
⇒ (QR + PR) × AB = (BC + AC) × PQ
⇒ (QR + PR) × 16 = (12 + 8) × 24
⇒ (QR + PR) × 16 = 20 × 24
⇒ QR + PR = 30
Thus, the answer is 30.
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