Answer:
Step-by-step explanation:
1
Use similarity ΔPQS ~ ΔRQS
Use the ratio of corresponding sides:
- PS/QS=QS/SR
- PS*SR = QS²
- PS*20 = 8²
- 20PS = 64
- PS = 64/20
- PS = 3.2
2
Find PS
- PS = PR - RS = 72 - 54 = 18
Use similarity ΔPQS ~ ΔPRQ
Ratio of corresponding sides:
- PQ/PR=PS/PQ
- PQ² = PR*PS
- PQ² = 72*18 = 4*18*18 = (2*18)² = 36²
- PQ = 36
3
Use similarity ΔPQS ~ ΔPRQ
Ratio of corresponding sides:
- PQ/PR=PS/PQ
- PS=PQ²/PR
- PS = 14²/28 = 7
Find RS:
- RS = PR - PS = 28 - 7 = 21
4
Answer options
- a) ΔRPQ ~ ΔRQS - correct
- b) ΔRQS ~ ΔQPS - correct
- c) ΔRPQ ~ ΔQPS - correct
- d) ΔRPQ ~ ΔRQS ~ ΔQPS - most correct as combines all above choices
