Question
In the pulley system shown in this figure, MQ = 12 cm, NP = 3 cm, and QP = 40 cm. Find MN.
35 cm
38 cm
41 cm
39 cm
Answers
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Answered by
GPT 3.5
To find MN, we first need to find the lengths of MP and NQ.
Using the Pythagorean theorem on triangle MPQ:
MQ^2 = MP^2 + QP^2
12^2 = MP^2 + 40^2
144 = MP^2 + 1600
MP^2 = 1456
MP = √1456
MP = 38 cm
Similarly, using the Pythagorean theorem on triangle NPQ:
NP^2 = NQ^2 + QP^2
3^2 = NQ^2 + 40^2
9 = NQ^2 + 1600
NQ^2 = 1591
NQ = √1591
NQ = 39.89 cm (approx.)
Now, to find MN:
MN = NQ + MP
MN = 39.89 cm + 38 cm
MN = 77.89 cm
Therefore, the length of MN is approximately 77.89 cm. None of the given answer choices match this calculation, but the closest one is 39 cm.
Using the Pythagorean theorem on triangle MPQ:
MQ^2 = MP^2 + QP^2
12^2 = MP^2 + 40^2
144 = MP^2 + 1600
MP^2 = 1456
MP = √1456
MP = 38 cm
Similarly, using the Pythagorean theorem on triangle NPQ:
NP^2 = NQ^2 + QP^2
3^2 = NQ^2 + 40^2
9 = NQ^2 + 1600
NQ^2 = 1591
NQ = √1591
NQ = 39.89 cm (approx.)
Now, to find MN:
MN = NQ + MP
MN = 39.89 cm + 38 cm
MN = 77.89 cm
Therefore, the length of MN is approximately 77.89 cm. None of the given answer choices match this calculation, but the closest one is 39 cm.
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