Let's solve this problem step-by-step to determine if the digital piano will fit along the wall next to the bookshelf in Robert's living room.
1. Understanding the Scale:
- The scale used in the drawing is 1 cm representing 6 inches in the actual room.
2. Actual Width of the Piano:
- The actual width of the digital piano is given as 54 inches.
3. Converting the Width to Scale:
- To find how wide the piano would appear on the scale drawing, we use the scale conversion:
[tex]\[
\text{Width of piano in drawing} = \frac{\text{Actual width of piano}}{\text{Scale factor}}
\][/tex]
- Plugging in the numbers:
[tex]\[
\text{Width of piano in drawing} = \frac{54 \text{ inches}}{6} = 9 \text{ cm}
\][/tex]
4. Available Length on the Drawing:
- Let's assume the available length along the wall next to the bookshelf in the scale drawing is already given as 10 cm.
5. Comparison:
- Now we compare the piano's width in the drawing to the available length in the drawing:
[tex]\[
9 \text{ cm} \leq 10 \text{ cm}
\][/tex]
- Since 9 cm (width of the piano in the drawing) is less than or equal to 10 cm (available space in the drawing), the piano will fit.
6. Conclusion:
- The digital piano will fit along the wall next to the bookshelf because its scaled width (9 cm) is less than the available length in the scale drawing (10 cm).
Therefore, Robert can confidently place the digital piano along the wall next to the bookshelf in his living room.
