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Trapezoid KLMN is dilated by a scale factor of
(1)/(4) to form trapezoid K'L'M'N'. Side L'M' measures 8. What is the measure of side LM?
Answer:

Trapezoid KLMN is dilated by a scale factor of $\frac{1}{4}$ to form trapezoid K'L'M'N'. Side L'M' measures $8$ . What is the measure of side LM? $\newline$ Answer:

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Dilations and parallel lines

Full solution

Q. Trapezoid KLMN is dilated by a scale factor of

\frac{1}{4}

to form trapezoid K'L'M'N'. Side L'M' measures

8

. What is the measure of side LM?

\newline

Answer:

Reverse Dilation Process: To find the measure of side $LM$ in the original trapezoid $KLMN$ , we need to reverse the dilation process. Since trapezoid $K'L'M'N'$ is a dilated version of $KLMN$ with a scale factor of $(1)/(4)$ , we can find the length of side $LM$ by dividing the length of side $L'M'$ by the scale factor. $\newline$ Calculation: $LM = \frac{L'M'}{(1/4)}$
Substitute Given Value: Now we substitute the given value of $L'M'$ into the equation. $\newline$ Calculation: $LM = \frac{8}{(1/4)}$
Multiply by Reciprocal: To divide by a fraction, we multiply by its reciprocal. So, we multiply $8$ by the reciprocal of $(1/4)$ , which is $4$ . $\newline$ Calculation: $LM = 8 \times 4$
Perform Multiplication: Perform the multiplication to find the length of side $LM$ . $\newline$ Calculation: $LM = 32$

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