Final answer:
To find how much carpet is required, determine the bedroom's area using the formula for the area of a rectangle: length × width. For a room measuring 14 feet by 11.5 feet, you'll need 161 square feet of carpet. When using scale drawings, ensure the accurate conversion of measurements to actual size.
Step-by-step explanation:
To calculate how much carpet is needed for a bedroom that is 14 feet long and 11.5 feet wide, we will use the algebraic formula for the area of a rectangle, which is length × width. In this case, the required carpet area will be 14 feet × 11.5 feet, which equals 161 square feet. Therefore, you would need 161 square feet of carpet to cover the bedroom floor.
Using a scale to calculate the area, as indicated by a scale factor of 1/24, is a different scenario. It means that one unit on the drawing represents 24 units in real life. To create a proportional equation, you would set up a ratio of scale to actual size, as in scale/actual. If the scale length and width are known, you can use these to find the actual length and width using this proportion. For example, if the scale width is 2, and the ratio is 2/w, we find the actual width (w) by solving this proportion.
In practical applications like this, it's important to specify the units you are working with. For instance, if you're making curtains, you'd need to convey the dimensions in a specific unit, such as meters, to the shop assistant to purchase the correct amount of fabric. Without the unit, the measurements would be ambiguous and possibly incorrect, just like in the scenario of making curtains for a doll's house versus actual windows.
Finally, a scaled diagram can be incredibly helpful when measuring rooms or buying materials. Creating a to-scale diagram requires measuring the actual length and width of the room and then converting these measurements using a chosen scale. This method can lead to accurate estimations of the amount of material needed for flooring, curtains, or other applications, as seen in the provided examples.