Question

polygon v is a scaled copy of polygon u.
what is the value of w?

Explanation:

Step1: Find the scale factor

Since polygon \(V\) is a scaled - copy of polygon \(U\), we can find the scale factor by comparing corresponding sides. Let's use the sides of length \(40\) (from polygon \(U\)) and \(36\) (from polygon \(V\)). The scale factor \(k\) is given by \(k=\frac{\text{side of }V}{\text{side of }U}\). So, \(k = \frac{36}{40}=\frac{9}{10}\)

Step2: Calculate the value of \(w\)

We know that the side of length \(30\) in polygon \(U\) corresponds to the side of length \(w\) in polygon \(V\). Using the formula \(w=\text{side of }U\times k\). Substitute the values: \(w = 30\times\frac{9}{10}\)

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Answer:

\(27\)