Questions: Find the length of KL.

Find the length of KL.
Transcript text: Find the length of KL.
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Solution

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Solution Steps

Step 1: Identify the given information

The trapezoid $FKLG$ has bases $KL$ and $FG$ with lengths $KL$ and $26$ respectively. It has one leg $GH = 16$. The trapezoid $KHLG$ has bases $KL$ and $GH$ and one leg $FL = FG = 26$.

Step 2: Use the midpoint theorem for trapezoids

If a segment connects the midpoints of the legs of a trapezoid, then it is parallel to each base and its length is one half the sum of the lengths of the bases. In this case, $GH$ connects the midpoints of the legs of trapezoid $FKLG$. $$GH = \frac{FG+KL}{2}$$

Step 3: Substitute known values and solve

$$16 = \frac{26 + KL}{2}$$ $$32 = 26+KL$$ $$KL = 32 - 26$$ $$KL = 6$$

Final Answer: The length of KL is 6.

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