The solutions for each case are listed below:
- TQ = 6, QR = 10, RP = 5
- RS = 36, RP = 81
- TQ = 8, RS = 2, PS = 1
- QR = 84, RS = 108 / 7, SP = 144 / 7
What are the missing lengths of two similar triangles?
Herein we find a geometrical system formed by two triangles similar to each other. Then, the following relationships are met:
PR = PS + SR
QR = QT + TR
RS / SP = RT / TQ
ST = √(RT² - RS²)
QP = √(QR² - RP²)
Now we proceed to determine the missing sides for each case:
Case A
RS = 2, SP = 3, RT = 4
TQ = RT × (SP / RS)
TQ = 4 × (3 / 2)
TQ = 6
QR = 6 + 4
QR = 10
RP = 3 + 2
RP = 5
Case B
SP = 45, RT = 32, RQ = 72, TQ = 40
RS = (RT / TQ) × SP
RS = (32 / 40) × 45
RS = 36
RP = 45 + 36
RP = 81
Case C
RP = 3, RT = 16, RQ = 24
TQ = QR - TR
TQ = 24 - 16
TQ = 8
PQ = √(QR² - RP²)
PQ = √(24² - 3²)
PQ = 9√7
RS / RP = RT / QR
RS = (RT / QR) × RP
RS = (16 / 24) × 3
RS = 2
PS = 3 - 2
PS = 1
Case D
RP = 36, RT = 36, TQ = 48
QR = 48 + 36
QR = 84
PQ = √(QR² - RP²)
PQ = √(84² - 36²)
PQ = 24√10
RS / RP = RT / RQ
RS = RP × (RT / RQ)
RS = 36 × (36 / 84)
RS = 108 / 7
SP = RP - RS
SP = 36 - 108 / 7
SP = 144 / 7
To learn more on similar triangles: https://brainly.com/question/25882965
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