Question

what is the value of z?
quadrilateral y is a scaled copy of quadrilateral x.
quadrilateral x
quadrilateral y

Explanation:

Step1: Find the scale factor

Since quadrilateral \(Y\) is a scaled - copy of quadrilateral \(X\), we can find the scale factor using the corresponding sides. Let's use the sides of length \(35\) and \(42\). The scale factor \(k=\frac{42}{35}=\frac{6}{5}\)

Step2: Calculate the value of \(z\)

We know that the side of length \(65\) in quadrilateral \(X\) corresponds to the side of length \(z\) in quadrilateral \(Y\). Using the scale factor \(k = \frac{6}{5}\), we have \(z=65\times\frac{6}{5}\)

$$z=\frac{65\times6}{5}=13\times6 = 78$$

Answer:

\(78\)