Question

question
\\(\overline{cd}\\) is dilated by a scale factor of \\(\frac{2}{3}\\) to form \\(\overline{cd}\\). \\(\overline{cd}\\) measures 32. what is the measure of \\(\overline{cd}\\)?
answer attempt 1 out of 2
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Explanation:

Step1: Set up the dilation formula

Let the length of $\overline{CD}$ be $x$. The dilation formula is $C'D'=\text{scale factor}\times CD$. We know that the scale factor is $\frac{2}{3}$ and $C'D' = 32$. So, $32=\frac{2}{3}x$.

Step2: Solve for $x$

Multiply both sides of the equation $32=\frac{2}{3}x$ by $\frac{3}{2}$. We get $x = 32\times\frac{3}{2}=\frac{96}{2}=48$.

Answer:

48