Math Snap

STEP 1

1. Triangle HIJ is similar to triangle H'I'J' due to dilation.
2. The scale factor of the dilation is $\frac{2}{3}$.
3. The side length $IJ$ of triangle HIJ is $42$.

STEP 2

1. Understand the relationship between the original and dilated triangles.
2. Apply the scale factor to the side length of the original triangle.
3. Calculate the length of side $I'J'$.

STEP 3

Understand the relationship between the original and dilated triangles:
Since triangle H'I'J' is a dilation of triangle HIJ, all corresponding sides of triangle H'I'J' are proportional to the sides of triangle HIJ by the scale factor $\frac{2}{3}$.

STEP 4

Apply the scale factor to the side length of the original triangle:
The side $IJ$ of triangle HIJ is $42$. To find the corresponding side $I'J'$ in triangle H'I'J', multiply $IJ$ by the scale factor:
$$I'J' = IJ \times \frac{2}{3}$$

Calculate the length of side $I'J'$:
$$I'J' = 42 \times \frac{2}{3}$$ $$I'J' = 28$$ The measure of side $I'J'$ is:
$$\boxed{28}$$