Question

quadrilateral y is a scaled copy of quadrilateral x.
quadrilateral x has sides 15, 35, 45 (and another side not fully labeled?); quadrilateral y has sides 18, 42, z (and another side). what is the value of z?

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. The side of length \(15\) in \(X\) corresponds to the side of length \(18\) in \(Y\).
The scale factor \(k=\frac{18}{15}=\frac{6}{5}\)

Step2: Calculate the value of \(z\)

The side of length \(45\) in \(X\) corresponds to the side of length \(z\) in \(Y\).
Using the scale factor, we have \(z = 45\times\frac{6}{5}\)

$$z=\frac{45\times6}{5}=9\times6 = 54$$

Answer:

\(54\)