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

The first blank is propyl 4 and the second is 2 (this is what I can tell if AB was 9 then PQ 3, so practically dividing by 3)

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:

$\frac{9}{3} =\frac{12}{QR}$

Cross multiplying and then solving gives us:

$9QR=3*12\\9QR=36\\QR=\frac{36}{9} \\QR=4$

To find RP, we use the proportion set below:

$\frac{9}{3} =\frac{6}{RP}$

Cross multiplying and then solving gives us:

$9RP=3*6\\9RP=18\\RP=\frac{18}{9} \\RP=2$

ANSWER:

QR is 4 units

RP is 2 units