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 $s'=k\times s$. Here, $k = \frac{3}{4}$, and we want to find $s$ (length of side $LI$) given $s'$ (length of side $L'I'$).

Step2: Identify the length of $L'I'$

From the diagram, the length of side $L'I'$ is $18$.

Step3: Solve for the original - side length

We know that $L'I'=k\times LI$. Rearranging the formula for $LI$, we get $LI=\frac{L'I'}{k}$. Substituting $L'I' = 18$ and $k=\frac{3}{4}$, we have $LI=\frac{18}{\frac{3}{4}}$.

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Answer:

$24$