Yani wants to make a scale diagram of the floor plan of his school. He wants his diagram to fit on an 8.5in. by 11in. sheet of paper. The school is 650ft long and 300 ft wide at its widest point.
a) what would be a reasonable scale for Yani to use so that his diagram will fit on the sheet of paper.
b) Assume that the school's floors plan is a rectangle.Draw a scale diagram using the scale you determined in park a)
1 inch = 65 feet
To determine a reasonable scale for Yani's diagram, we need to calculate how much smaller the actual dimensions will be on the sheet of paper.
a) Let's calculate the reduction ratio for the length and width separately:
Reduction Ratio for Length:
Actual length of the school = 650 ft
Length of the paper = 8.5 in
Conversion factor (to convert feet to inches) = 12 (1 ft = 12 in)
Scaled down length = Length of the paper / Conversion factor
= 8.5 in / 12
= 0.7083 ft
Reduction ratio for length = Scaled down length / Actual length
= 0.7083 ft / 650 ft
≈ 0.001089
Reduction Ratio for Width:
Actual width of the school = 300 ft
Width of the paper = 11 in
Scaled down width = Width of the paper / Conversion factor
= 11 in / 12
= 0.9167 ft
Reduction ratio for width = Scaled down width / Actual width
= 0.9167 ft / 300 ft
≈ 0.0030567
Thus, a reasonable scale for Yani's diagram would be approximately 1:1000, as this will allow the floor plan to fit on an 8.5in. by 11in. sheet of paper.
b) Now, let's draw the scale diagram using the scale of 1:1000:
To draw the diagram, we'll represent 1 ft on the floor plan as 0.001 inches on the paper.
For the length, we scale down the actual length of the school (650 ft) by multiplying it by the scale factor:
Scaled length = Actual length * Scale factor
= 650 ft * 0.001
= 0.65 inches
For the width, we scale down the actual width of the school (300 ft):
Scaled width = Actual width * Scale factor
= 300 ft * 0.001
= 0.3 inches
Now, using a ruler or straight edge, draw a rectangle on the paper measuring 0.65 inches by 0.3 inches to represent the floor plan of the school.
To determine a reasonable scale for Yani's scale diagram, we need to consider the dimensions of the school and the size of the paper.
a) Let's start with the length of the school, which is given as 650 ft. The length of the paper is 8.5 inches. We need to find a ratio between these two values. To convert feet to inches, we multiply by 12 because there are 12 inches in a foot.
650 ft * 12 inches/foot = 7800 inches
Now, we can calculate the scale factor by dividing the length of the paper by the actual length of the school:
Scale factor = length of paper / actual length of school
Scale factor = 8.5 inches / 7800 inches
Now, we can simplify the scale factor:
Scale factor = 1 / (7800/8.5)
Scale factor ≈ 1 / 917.647
Scale factor ≈ 0.00109
So, a reasonable scale for Yani to use would be 1:0.00109 or 1 inch on the paper represents approximately 0.00109 inches in reality.
b) To draw a scale diagram, we will use the scale factor of 1:0.00109. Since the school's floor plan is a rectangle, we can simply draw a rectangle on the paper, keeping the proportions of the original dimensions intact.
Let's represent the length of the school (650 ft) and the width at its widest point (300 ft) using the scale factor:
Length = 650 ft * 0.00109 = 0.7095 inches
Width = 300 ft * 0.00109 = 0.327 inches
On the sheet of paper, draw a rectangle with a length of 0.7095 inches and a width of 0.327 inches to create a scale diagram of the school's floor plan.