Q8 of 62 Page 186

The lengths of three sides of a triangle ABC are 6 cm, 4 cm and 9 cm. ΔPQR ~ ΔABC. One of the lengths of sides of ΔPQR is 35cm. What is the greatest perimeter possible for ΔPQR?


One of the length should be 35cm.


So, for perimeter to be greatest the smallest length of PQR should be 35 cm so that the other 2 sides could be greater than 35 cm hence greatest Perimeter achieved in that case.


ΔPQR ∼ ΔABC (given)


⇒ PQ = 35 cm (∵ It corresponds AB which is the smaller side of ΔABC)




⇒ PR = 52.5 cm




⇒ QR = 78.75 cm


⇒ Perimeter = PQ + PR + QR


⇒ Perimeter = 35 + 52.5 + 78.75


⇒ Perimeter = 166.25 cm


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