Question

polygon f is a scaled copy of polygon e.
what is the value of d?

Explanation:

Step1: Find the scale factor

Since polygon \(F\) is a scaled copy of polygon \(E\), we find the scale factor by dividing the corresponding side lengths of \(F\) and \(E\). The scale factor \(k=\frac{\frac{9}{10}}{\frac{3}{4}}\).
Using the rule for dividing fractions \(\frac{a}{b}\div\frac{c}{d}=\frac{a\times d}{b\times c}\), we have \(k = \frac{9}{10}\times\frac{4}{3}=\frac{9\times4}{10\times3}=\frac{36}{30}=\frac{6}{5}\).

Step2: Calculate the value of \(d\)

We know that \(d\) is related to \(\frac{4}{9}\) by the scale factor. So \(d=\frac{4}{9}\times k\).
Substitute \(k = \frac{6}{5}\) into the equation: \(d=\frac{4}{9}\times\frac{6}{5}\).
Using the rule for multiplying fractions \(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\), we get \(d=\frac{4\times6}{9\times5}=\frac{24}{45}=\frac{8}{15}\).

Answer:

\(\frac{8}{15}\)