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.
Answer:
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
