Question

ΔABC is similar to ΔPQR. AB¯¯¯¯¯ corresponds to PQ¯¯¯¯¯, and BC¯¯¯¯¯ corresponds to

QR¯¯¯¯¯. If AB = 9, BC = 12, CA = 6, and PQ = 3, what are the lengths of QR¯¯¯¯¯ and RP¯¯¯¯¯?


a QR = 4, RP = 2


b QR = 6, RP = 4.5


c QR = 4.5, RP = 6


d QR = 2, RP = 4

Answer 1

Heya user ,
Here is your answer !!

ΔABC is similar to ΔPQR.
AB corresponds to PQ,
and BC corresponds to QR.
So, AC corresponds to PR .

Hence ,
AB/PQ = BC/QR = AC/PR .

GIVEN ,
AB = 9, BC = 12, CA = 6, and PQ = 3 .

ATQ ,
AB/PQ = BC/QR
=> 9/3 = 12/QR
=> QR = 4

Also,
AB/PQ = AC/PR
=> 9/3 = 6/PR
=> PR = 2 .

Hence ,

Answer is option (A) QR = 4, RP = 2 .

Hope it helps !!