Question

hexagon g is a scaled copy of hexagon f. what is the value of h?

Explanation:

Step1: Find the scale - factor

Since hexagon G is a scaled copy of hexagon F, the ratio of corresponding side - lengths is the same. Let the scale - factor be \(k\). We can find \(k\) by comparing the known corresponding side - lengths. The known side - length of hexagon F is \(1\frac{1}{4}=\frac{5}{4}\) and the corresponding side - length of hexagon G is \(2\frac{1}{2}=\frac{5}{2}\). Then \(k=\frac{\text{side of G}}{\text{side of F}}=\frac{\frac{5}{2}}{\frac{5}{4}}\).
\[k = \frac{5}{2}\times\frac{4}{5}=2\]

Step2: Calculate the value of \(h\)

The side - length of hexagon F corresponding to \(h\) is \(\frac{9}{10}\). To find \(h\), we multiply the side - length of hexagon F by the scale - factor \(k\). So \(h=\frac{9}{10}\times k\). Substitute \(k = 2\) into the equation.
\[h=\frac{9}{10}\times2=\frac{9}{5} = 1\frac{4}{5}\]

Answer:

\(1\frac{4}{5}\)