At the half time show during a football game, a marching band is to form a rectangle 50yards by 16yards. The conductor wants to plan out the band members positions using a 14- by 8.5-in. sheet of paper. What scale should she use to fir both dimensions of the rectangle on the page? (Use whole inches and yards)
50/14 = 3.57
so a scale of 1 in:4 yds would work for the length
16/8.5 = 1.88
so a scale of 1 in:2 yds would work for the width.
Looks like 1 in = 4 yds is the ticket.
To determine the scale at which the conductor should draw the rectangle on the sheet of paper, we need to find the ratio between the dimensions of the rectangle and the dimensions of the paper.
1. Convert the dimensions of the rectangle from yards to inches:
- Length: 50 yards = 50 * 36 inches = 1800 inches
- Width: 16 yards = 16 * 36 inches = 576 inches
2. Calculate the ratio between the dimensions of the rectangle and the dimensions of the paper:
- Length ratio: 1800 inches / 14 inches
- Width ratio: 576 inches / 8.5 inches
3. Simplify the ratios:
- Length ratio: 1800 / 14 = 128.6 ≈ 129
- Width ratio: 576 / 8.5 ≈ 67.8 ≈ 68
Therefore, the conductor should use a scale of 129:1 for the length and 68:1 for the width to fit the entire rectangle on the 14- by 8.5-in. sheet of paper.
To determine the scale needed to fit both dimensions of the rectangle on the 14- by 8.5-in. sheet of paper, we first need to convert the measurements to the same unit. In this case, we will convert everything to inches.
The given dimensions of the rectangle are 50 yards by 16 yards. Since there are 3 feet in a yard, we can convert yards to feet by multiplying by 3:
50 yards * 3 feet/yard = 150 feet
16 yards * 3 feet/yard = 48 feet
Since there are 12 inches in a foot, we can convert feet to inches by multiplying by 12:
150 feet * 12 inches/foot = 1800 inches
48 feet * 12 inches/foot = 576 inches
Now that we have both dimensions of the rectangle in inches, we can compare them to the dimensions of the paper.
We have a 14- by 8.5-in. sheet of paper. Let's compare the lengths of the rectangle and the paper:
1800 inches (rectangle length) / 14 inches (paper length) = 128.57
Similarly, let's compare the widths of the rectangle and the paper:
576 inches (rectangle width) / 8.5 inches (paper width) = 67.76
To find the appropriate scale, we need to determine the highest common factor of the two ratios. In this case, the highest common factor is 1.
Therefore, the rectangle cannot fit entirely on the sheet of paper with whole inches.
In conclusion, there is no whole-inch scale that can be used to fit both dimensions of the rectangle on the 14- by 8.5-in. sheet of paper. You may need a larger sheet of paper or consider using a different scale, such as half-inch or quarter-inch scale.