Area of ∆ABC = 36,
Area of ∆ABC = 36,Area of ∆PQR = 64
Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12
Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12The correspondence ABC ↔ PQR is a similarity.
Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12The correspondence ABC ↔ PQR is a similarity.To find: PQ = ?
Area of ∆ABC = 36,Area of ∆PQR = 64AB = 12The correspondence ABC ↔ PQR is a similarity.To find: PQ = ?For this,
Recall the property,
Ratio of areas of two similar triangles = Ratio of squares of the corresponding sides
Area of ∆PQR / Area of ∆ABC =(PQ/AB)²
64 /36 = (PQ/AB)²
(PQ/AB) = √64 /36
(PQ/AB)= 8/6
PQ=AB ×8/6
PQ = 12×8/6
⇒ PQ = 2 × 8
⇒ PQ = 2 × 8⇒ PQ = 16
⇒ PQ = 2 × 8⇒ PQ = 16Thus, answer is 16.