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Mhanifaidn

Answer:

  • See below

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
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