Question

Trapezoid IJKL is dilated by a scale factor of start fraction, 2, divided by, 3, end fraction
3
2
​
to form trapezoid I'J'K'L'. Side I'J' measures 44. What is the measure of side IJ?

Answer 1

To find the measure of side \( IJ \) in trapezoid \( IJKL \) given that trapezoid \( I'J'K'L' \) is a dilation of trapezoid \( IJKL \) by a scale factor of \( \frac{2}{3} \), and that side \( I'J' \) measures 44, we can use the relationship between the original and the dilated figures.

The relationship can be represented as follows:

\[
I'J' = \text{scale factor} \times IJ
\]
Given:
- \( I'J' = 44 \)
- scale factor = \( \frac{2}{3} \)

Substituting into the equation, we have:

\[
44 = \frac{2}{3} \times IJ
\]

To solve for \( IJ \), we can rearrange the equation:

\[
IJ = 44 \div \frac{2}{3} = 44 \times \frac{3}{2}
\]

Calculating \( IJ \):

\[
IJ = 44 \times \frac{3}{2} = 44 \times 1.5 = 66
\]

Thus, the measure of side \( IJ \) is \( \boxed{66} \).