In the figure shown (sorry no diagram, but description below), NK and ML are parallel, JN=10 feet, NK=14 feet, JL=22 feet, and ML=24. Find KL.

Its a triangle with JN and NM on the left side and JK and KL on the right side. NK is a horizontal line in the middle of the triangle. The triangle isn't equilateral.

To find the length of KL, we need to use the properties of parallel lines and triangles. Here's how you can solve this problem:

Step 1: Understand the given information
From the description, we know that NK and ML are parallel. We also have the following measurements:
- JN = 10 feet
- NK = 14 feet
- JL = 22 feet
- ML = 24 feet

Step 2: Identify the triangles involved
To find KL, we need to look at the triangles involved in the figure. In this case, we can focus on two triangles: triangle NKL and triangle JML.

Step 3: Apply the properties of parallel lines
Since NK and ML are parallel, we can use the property known as the "Alternate Interior Angle Theorem". According to this theorem, if a transversal (JL, in this case) intersects two parallel lines (NK and ML), then the corresponding angles are equal.

Step 4: Determine the missing angles
Now, let's examine triangle JML. Since NK and ML are parallel, we can see that angle JML and angle K are corresponding angles and therefore equal.

Step 5: Find the missing side using similar triangles
Using triangle JML and triangle NKL, we can see that they are similar triangles because they share angles J and L. Recall that in similar triangles, corresponding sides are proportional.

Since JL is known to be 22 feet and ML is known to be 24 feet, we can set up a proportion with these lengths:
JL/ML = JN/NK

Plugging in the known values, we get:
22/24 = 10/KL

Step 6: Solve for KL
To find KL, we need to solve the proportion we set up in the previous step.
Cross-multiplying, we get: 22 × KL = 24 × 10
Simplifying further, we have: 22 × KL = 240

Dividing both sides by 22, we find: KL = 240/22 ≈ 10.91 feet

Therefore, the length of KL is approximately 10.91 feet.