Question

ANSWER QUICKLY PLEASE!!!!!!

Answer 1

• See below

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