Question

parallelogram d is a scaled copy of parallelogram c. what scale factor takes parallelogram c to parallelogram d?

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) from the original figure (parallelogram \(C\)) to the scaled - copy (parallelogram \(D\)) is given by \(k=\frac{\text{corresponding side length of scaled - copy}}{\text{corresponding side length of original}}\).

Step2: Identify corresponding side lengths

We can use either the pair of side lengths \(15\) (from parallelogram \(C\)) and \(9\) (from parallelogram \(D\)) or \(45\) (from parallelogram \(C\)) and \(27\) (from parallelogram \(D\)).
Using the first pair: \(k = \frac{9}{15}\).
Simplify \(\frac{9}{15}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(3\). So, \(\frac{9\div3}{15\div3}=\frac{3}{5}\).
Using the second pair: \(k=\frac{27}{45}\).
Simplify \(\frac{27}{45}\) by dividing both the numerator and the denominator by \(9\). So, \(\frac{27\div9}{45\div9}=\frac{3}{5}\).

Answer:

\(\frac{3}{5}\)