In the pulley system shown in this figure, MQ=10 in., NP=3 in., and QP=24 in. Find MN
a. 25
b. 26
c. 27
d. 28
We can not see the figure.
Since I can't post URLs, here is the description
There is one large circle and one small circle, connected by two lines.
M splits the circle by two, whilst N splits the other circle by two.
Angle M is approximately 160 degrees whilst the other is also 160
To solve this question, we can use the concept of similar triangles, which states that corresponding sides of similar triangles are proportional.
In the given figure, triangles QPM and NMQ are similar. This means that their corresponding sides are proportional.
Let's set up a proportion using the corresponding sides:
QP / MN = QM / NP
Substituting the given values, we have:
24 / MN = 10 / 3
To solve for MN, we can cross-multiply:
10 * MN = 24 * 3
Simplifying, we get:
10 * MN = 72
Now, divide both sides by 10 to isolate MN:
MN = 72 / 10
Calculating the value, we find:
MN = 7.2
Since the answer choices are all whole numbers, we need to round the result.
Rounding 7.2 to the nearest whole number gives us:
MN ≈ 7
Therefore, the correct answer is option b. 26.