∆ABC is similar to ∆PQR. Corresponds to , and corresponds to . If the length of is 9 units, the length of is 12 units, the length of is 6 units, and the length of is 3 units, then the length of is

Complete 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.

QR = 4 units ; RP = 2 units

Step-by-step explanation:

For similar triangles

Length1 ∆1/length1 ∆2 = Length 2 ∆1 /length 2∆2

AB Corresponds to PQ

BC corresponds to QR

AB = 9 Units, BC = 12 Units

CA = 6 units, PQ = 3 units

Take the ratio of the corresponding sides :

AB/ PQ = BC / QR

9/ 3 = 12 / QR

Cross multiply

9 * QR = 3 * 12

QR = 36 / 9

QR = 4 units

For RP:

AB/PQ = CA/RP

9 / 3 = 6 / RP

9 * RP = 3 * 6

RP = 18 / 9

RP = 2 units

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