Question

hexagon u is a scaled copy of hexagon t.
hexagon t
hexagon u
what is the value of z?

Explanation:

Step1: Find the scale factor

Since hexagon \(U\) is a scaled copy of hexagon \(T\), the ratio of corresponding sides is the same. The side of length \(3.6\) in hexagon \(T\) corresponds to the side of length \(2.7\) in hexagon \(U\). The scale factor \(k=\frac{2.7}{3.6}=\frac{27}{36}=\frac{3}{4}\)

Step2: Calculate the value of \(z\)

The side of length \(2.4\) in hexagon \(T\) corresponds to the side of length \(z\) in hexagon \(U\). Using the scale factor \(k = \frac{3}{4}\), we have \(z=2.4\times\frac{3}{4}\)

$$z=\frac{2.4\times3}{4}=\frac{7.2}{4}=1.8$$

Answer:

\(1.8\)