Question

polygon l is a scaled copy of polygon k.
polygon k (green) has side lengths 48 (top), 40 (right), 28 (bottom right).
polygon l (blue) has side lengths 36 (top), 30 (right), m (bottom right).
what is the value of m?
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Explanation:

Step1: Find the scale factor

Since polygon \( L \) is a scaled copy of polygon \( K \), the ratio of corresponding sides should be equal. Let's take the top sides: \( \frac{36}{48}=\frac{3}{4} \). We can check with another pair: \( \frac{30}{40}=\frac{3}{4} \), so the scale factor is \( \frac{3}{4} \).

Step2: Calculate \( m \)

The side of length 28 in polygon \( K \) corresponds to side \( m \) in polygon \( L \). So we use the scale factor: \( m = 28\times\frac{3}{4} \).
Simplify: \( 28\times\frac{3}{4}=\frac{84}{4} = 21 \).

Answer:

21