Final answer:
To find JK, we can use the concept of midsegments in triangles and set up a proportion. Solving the proportion, we find that JK is equal to 20 units. Therefore, the correct option is b).
Step-by-step explanation:
To find JK, we need to understand the concept of midsegments in triangles. A midsegment is a line connecting the midpoints of two sides of a triangle. In this case, MN, NP, and MP are midsegments.
As midsegments, MN and NP are parallel to the third side JK. Therefore, we can say that MN is parallel to JK and NP is parallel to JK.
The ratio of the lengths of parallel sides in a triangle is equal to the ratio of the lengths of corresponding midsegments. In this case, we can set up the following proportion:
MN/JK = NP/MP
Substituting the given values, we have:
24/JK = 13/17
Cross multiplying, we get:
13JK = 24*17
Dividing both sides by 13, we find JK = 24*17/13
= 20 units
Therefore, the correct option is b).