The Community Recreation Center is developing plans for a new sports facility.
Community members can submit suggestions for the new facility, along with basic scale drawings of their ideas.
Elena wants to include a new 15- by 30-meter basketball court in the athletic center. She is submitting a scale drawing on an 8.5- by 11-inch sheet of paper. Which scale should Elena use to create as large a drawing as possible on the paper?
longest dimensions: 30m and 11 in paper. So make one inch 3 m
that will make the drawing
5inches x 10 inches
To determine the scale that Elena should use to create as large a drawing as possible on an 8.5- by 11-inch sheet of paper, we need to compare the size of the basketball court to the size of the paper.
The size of the basketball court is given as 15 by 30 meters.
The size of the paper is given as 8.5 by 11 inches, which is equivalent to approximately 0.2159 by 0.2794 meters.
To determine the appropriate scale, we need to divide the size of the basketball court by the size of the paper.
For the width scale:
15 meters ÷ 0.2159 meters = 69.46
For the length scale:
30 meters ÷ 0.2794 meters = 107.33
The scale that Elena can use to create as large a drawing as possible on the paper is 1:69.46 for the width and 1:107.33 for the length.
To determine the scale Elena should use to create as large a drawing as possible on an 8.5- by 11-inch sheet of paper, we need to consider the dimensions of the basketball court and the dimensions of the paper.
Elena wants to include a 15- by 30-meter basketball court in her drawing. We need to convert these dimensions to inches since the paper size is given in inches.
1 meter is equal to approximately 39.37 inches. Therefore, the dimensions of the basketball court in inches are:
15 meters * 39.37 inches/meter = 590.55 inches (approximately)
30 meters * 39.37 inches/meter = 1181.1 inches (approximately)
Next, we need to determine how many times these dimensions can fit within the 8.5- by 11-inch paper.
Since Elena wants to create as large a drawing as possible on the paper, she should use the largest scale that allows the basketball court to fit within the paper.
Let's calculate the scales using the dimensions of the basketball court and the paper:
Scale for the width:
8.5 inches (paper width) / 590.55 inches (basketball court width) ≈ 0.014 (approximately)
Scale for the length:
11 inches (paper length) / 1181.1 inches (basketball court length) ≈ 0.0093 (approximately)
Now, we have two scales: 0.014 for the width and 0.0093 for the length. Since the scale should be consistent for both dimensions, Elena should choose the smaller scale, which is 0.0093.
Therefore, Elena should use a scale of 1:0.0093 on her 8.5- by 11-inch sheet of paper to create as large a drawing as possible of the 15- by 30-meter basketball court.