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⎯⎯⎯⎯⎯?

Answer 1

QR = 4, RP = 2. Remember that fraction is also known as ratio. So use steps/formulas as per necessary. U can also use algebra ☺

Answer 2

/QR/ = 4 and /RP/ = 2.

Explanation:

Comparing the two triangles,

`(/AB/)/(/BC/)` =
`(/PQ/)/(/QR/)`

⇒
`(9)/(12)` =
`(3)/(/QR/)`

/QR/ = 4

Also,

`(/AB/)/(/AC/)` =
`(/PQ/)/(/PR/)`

⇒
`(9)/(6)` =
`(3)/(/PR/)`

/RP/ = 2

Therefore, /QR/ = 4, /RP/ = 2.