A room measures 12 feet by 15 feet. find the scale that would allow the room to be shown as large as possible on a piece of paper. explain your reasoning.
paper probably is 8.5 by 11 inches
8.5/12 = .708 inches per foot
11/15 = .733 inches per foot
so the width sets the boundary
say 0.7 inches/foot
then 12 feet comes out 8.4 inches
and 15 feet comes out 10.5 inches
if they want a scale ratio instead of inches per foot it would be
.7 inches /foot * 1/12 foot/inch = .058 feet paper/foot model or the inverse is 17.1 feet of room to 1 foot of paper
What is the size of the piece of paper?
7 in by 8 in
So I have problem that say 12feet by 15 for the actual measurements on floor plan
To find the scale that would allow the room to be shown as large as possible on a piece of paper, we need to consider the size of the room and the size of the paper.
First, let's determine the size of the room in relation to the paper. The room measures 12 feet by 15 feet. Suppose we assume that the longer side of the paper will represent the longer side of the room. Therefore, the ratio of the longer side of the room to the longer side of the paper will determine the scale.
Next, let's consider the size of the paper. Paper sizes are typically standardized, with one common option being 8.5 inches by 11 inches (letter size). However, paper sizes may vary, so it's important to know the specific dimensions of the paper you'll be using.
In this example, let's assume we are using letter-sized paper with dimensions of 8.5 inches by 11 inches.
Now, we can calculate the scale. Since the room measures 12 feet by 15 feet, we need to convert these measurements to inches to match the paper size.
12 feet = 12 feet * 12 inches/foot = 144 inches
15 feet = 15 feet * 12 inches/foot = 180 inches
We can compare the dimensions of the room in inches to the dimensions of the paper to find the scale.
For the longer side (15 feet), the ratio would be 180 inches (room) / 11 inches (paper) ≈ 16.36.
For the shorter side (12 feet), the ratio would be 144 inches (room) / 8.5 inches (paper) ≈ 16.94.
Since we want to maximize the size of the room on the paper, we should choose the larger of the two ratios, which is approximately 16.94.
Therefore, the scale that would allow the room to be shown as large as possible on the paper is 1:16.94, meaning that 1 inch on the paper represents approximately 16.94 inches in the real room.