Question

the segment below is the image of $overline{kl}$ after dilation by a scale factor of $\frac{3}{4}$. what is the measure of $overline{kl}$?

Explanation:

Step1: Recall dilation formula

Let the length of $\overline{KL}$ be $x$. The length of the dilated segment $\overline{K'L'}$ is related to the original segment by the formula $K'L'= \text{scale - factor}\times KL$. Here, $K'L' = 21$ and the scale - factor is $\frac{3}{4}$. So, $21=\frac{3}{4}x$.

Step2: Solve for $x$

To solve for $x$, we use the equation $21=\frac{3}{4}x$. Multiply both sides of the equation by $\frac{4}{3}$ to isolate $x$. So, $x = 21\times\frac{4}{3}$.
$21\times\frac{4}{3}=\frac{21\times4}{3}=\frac{84}{3}=28$.

Answer:

28