Question

∆ABC is similar to ∆PQR. AB¯¯¯¯¯ corresponds to PQ¯¯¯¯¯, and BC¯¯¯¯¯ corresponds to QR¯¯¯¯¯. If the length of AB¯¯¯¯¯ is 9 units, the length of BC¯¯¯¯¯ is 12 units, the length of CA¯¯¯¯¯ is 6 units, and the length of PQ¯¯¯¯¯ is 3 units, then the length of QR¯¯¯¯¯ is ______units and the length of RP¯¯¯¯¯ is ________units.

Answer 1

QR- 4, RP- 2

Explanation:

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Answer 2

See the attached picture.

Since ABC is similar to PQR, the corresponding sides' ratio are same.

To find QR, we use the proportion set below:

`(9)/(3) =(12)/(QR)`

Cross multiplying and then solving gives us:

`9QR=3*12\\9QR=36\\QR=(36)/(9) \\QR=4`

To find RP, we use the proportion set below:

`(9)/(3) =(6)/(RP)`

Cross multiplying and then solving gives us:

`9RP=3*6\\9RP=18\\RP=(18)/(9) \\RP=2`

ANSWER:

QR is 4 units

RP is 2 units