1. **Stating the problem:** We have an L-shaped figure with dimensions given: the long horizontal part is 46 mm long and 12 mm high, the vertical segment is 30 mm high and 5 mm wide. We want to find the lengths of $x'$ and $y'$ as indicated by the red arrows. 2. **Understanding the figure:** - $x'$ is the horizontal distance from the inside corner to the left end of the horizontal part. - $y'$ is the vertical distance from the horizontal part down to the bottom of the vertical part. 3. **Calculating $x'$:** - The total horizontal length is 46 mm. - The vertical segment has a width of 5 mm, which intrudes into the horizontal length. - Therefore, $x' = 46 - 5 = 41$ mm. 4. **Calculating $y'$:** - The total vertical height of the vertical segment is 30 mm. - The horizontal part has a height of 12 mm. - So, $y' = 30 - 12 = 18$ mm. 5. **Final answers:** $$x' = 41 \text{ mm}$$ $$y' = 18 \text{ mm}$$