A lacrosse field measures 110 yards long by 60 yards wide. What would be an appropriate scale to construct a scale drawing of a lacrosse field so it would best fit on a 8.5 by 11 inch sheet of paper?(1 yd = 36 in.)
A rectangular soccer field measures 110 yards long and 70 yards wide. What is the area of the soccer field?
To determine an appropriate scale for the scale drawing, we need to consider two factors: the actual size of the lacrosse field and the size of the paper.
The length of the lacrosse field is given as 110 yards, which is equivalent to 110 * 36 = 3960 inches.
The width of the lacrosse field is given as 60 yards, which is equivalent to 60 * 36 = 2160 inches.
The size of the paper is 8.5 inches by 11 inches.
To fit the lacrosse field on the paper, we need to find a scale that reduces the size of the field to fit within the paper's dimensions.
Let's determine the appropriate scale for the length of the field:
Scale factor = (Length of the field in inches) / (Length of the paper)
Scale factor = 3960 / 8.5
Scale factor = 466.28
Next, let's determine the appropriate scale for the width of the field:
Scale factor = (Width of the field in inches) / (Width of the paper)
Scale factor = 2160 / 11
Scale factor = 196.36
Since we want to use the same scale for both the length and width of the field, we need to choose a scale that will work for both.
The largest scale factor is 466.28, so we will use that as our scale.
Therefore, an appropriate scale for the scale drawing of the lacrosse field would be 1 inch = 466.28 inches.
To determine the appropriate scale for the scale drawing, we need to consider the size of the lacrosse field and the size of the paper. Let's work through the steps:
1. Determine the dimensions of the lacrosse field in inches:
- Length: 110 yards * 36 inches/yard = 3960 inches
- Width: 60 yards * 36 inches/yard = 2160 inches
2. Decide on the dimensions of the paper:
- Length: 11 inches
- Width: 8.5 inches
3. Calculate the scale factor by comparing the field dimensions to the paper dimensions:
- Scale factor for length = Paper length / Field length = 11 inches / 3960 inches
- Scale factor for width = Paper width / Field width = 8.5 inches / 2160 inches
4. Simplify the scale factors:
- Scale factor for length = 1/360
- Scale factor for width = 1/240
5. Express the scale factors in the form of a fraction or a ratio:
- Scale factor for length: 1 inch on the paper represents 360 inches on the field.
- Scale factor for width: 1 inch on the paper represents 240 inches on the field.
Therefore, an appropriate scale to construct a scale drawing of the lacrosse field that will fit on an 8.5 by 11 inch sheet of paper would be 1 inch representing 360 inches for the length and 1 inch representing 240 inches for the width.
Align the 110 yard dimension of the field with the 11 inch dimension of the paper, and center the field in the middle of the page. You can make the figure bigger that way. There will be more than enough width on the paper for the other dimension.
I recommend a scale of about 12 yards per inch. That will make the length dimension 9.17 inches on the paper