Question

quadrilateral ijkl is dilated by a scale factor of $\frac{3}{4}$ to form quadrilateral ijkl. what is the measure of side li?

Explanation:

Step1: Recall dilation formula

If a figure is dilated by a scale - factor $k$, the length of a side of the original figure $s$ and the length of the corresponding side of the dilated figure $s'$ are related by the formula $s'=ks$. Here, we want to find the length of the side in the original figure, so we can rewrite the formula as $s = \frac{s'}{k}$. The scale factor $k=\frac{3}{4}$, and we assume the length of the corresponding side $L'I'$ in the dilated figure is $20.1$.

Step2: Substitute values into formula

Substitute $s' = 20.1$ and $k=\frac{3}{4}$ into the formula $s=\frac{s'}{k}$. We get $s=\frac{20.1}{\frac{3}{4}}$.

Step3: Simplify the expression

To divide by a fraction, we multiply by its reciprocal. So $s = 20.1\times\frac{4}{3}$. First, $20.1=\frac{201}{10}$. Then $\frac{201}{10}\times\frac{4}{3}=\frac{201\times4}{10\times3}=\frac{804}{30}=26.8$.

Answer:

$26.8$