Question

polygon z is a scaled copy of polygon y.
diagrams: polygon y has side lengths \\(\frac{9}{10}\\), \\(\frac{9}{8}\\), \\(\frac{9}{8}\\); polygon z has side lengths \\(x\\), \\(\frac{3}{4}\\), \\(\frac{3}{4}\\).
what is the value of (x)?

Explanation:

Step1: Find the scale factor

Since polygon Z is a scaled copy of polygon Y, we can find the scale factor by dividing the corresponding side lengths of Z by Y. Let's take the vertical side: the length in Y is $\frac{9}{8}$ and in Z is $\frac{3}{4}$. So the scale factor $k = \frac{\frac{3}{4}}{\frac{9}{8}}$.
Simplify: $k=\frac{3}{4}\times\frac{8}{9}=\frac{24}{36}=\frac{2}{3}$.

Step2: Use the scale factor to find x

The corresponding top side in Y is $\frac{9}{10}$, so in Z (which is x), we multiply by the scale factor. So $x = \frac{9}{10}\times\frac{2}{3}$.
Simplify: $x=\frac{18}{30}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$