A giant football field is made for the floor of the gym. The length of the gym is 90 feet. Using this same scale, determine the width of the paper football field. How do I solve this if it says that the dimensions are 160 ft? by 360 ft. and the end zone is 160 ft. by 30 ft. and the upright goalpost is 10 ft. off the ground, and the width of the upright is 18 ft. 6 in.
90 ft is one quarter of the actual field length ... 90/360 = 1/4
so multiply all of the actual dimensions by 1/4 to find the scaled dimensions
To determine the width of the paper football field, we need to use the given scale. The length of the gym is 90 feet, and the corresponding dimension of the gym floor on the paper is given as 160 feet.
Since the dimensions of the gym floor and the paper football field are directly proportional, we can set up a proportion to solve for the width of the paper football field.
Let's represent the width of the paper football field as "x".
Using the proportion:
Length of the gym floor / Width of the gym floor = Length of the paper football field / Width of the paper football field
90 feet / x = 160 feet / 360 feet
To solve for x, we can cross-multiply:
90 feet * 360 feet = 160 feet * x
32,400 = 160x
Dividing both sides by 160:
x = 32,400 / 160
x = 202.5 feet
Therefore, the width of the paper football field, using the given scale, is 202.5 feet.
Moving on to the other information provided:
- The end zone is given dimensions of 160 ft. by 30 ft. These dimensions remain the same on the paper football field since no scale is mentioned specifically for the end zone.
- The upright goalpost is mentioned to be 10 ft. off the ground, and the width of the upright is 18 ft. 6 in.
Considering the 10 ft. height off the ground, this corresponds to a specific height on the paper football field according to the scale mentioned earlier. To find the corresponding height on the paper, we can use the same proportion as before:
90 feet / h = 10 feet / 18.5 feet
Simplifying:
90 * 18.5 = 10h
1,665 = 10h
Dividing both sides by 10:
h = 166.5 feet
So, the height of the upright goalpost on the paper football field would be 166.5 feet.
Hope this helps!
To determine the width of the paper football field, we need to use the given scale. Since the length of the gym is 90 feet, we can set up a proportion to find the corresponding width of the paper football field.
Given:
Length of the gym: 90 feet
Length of the paper football field: 160 feet
Let's set up the proportion:
Gym length / Paper field length = Gym width / Paper field width
Substituting the given values, we get:
90 feet / 160 feet = Gym width / Paper field width
To solve for the width of the paper field, cross multiply and then divide:
90 feet * Paper field width = 160 feet * Gym width
Paper field width = (160 feet * Gym width) / 90 feet
Now, we need to determine the value of Gym width. Given the dimensions, the gym width is not provided directly. However, the information about the end zone and the upright goalpost can help us solve for it.
Given:
End zone length: 160 feet
End zone width: 30 feet
Upright goalpost height: 10 feet
Upright width: 18 ft. 6 in.
The total width of the gym can be calculated by adding the width of the end zone to the width of the upright goalpost on each side.
Total gym width = (end zone width + upright width) + (end zone width + upright width)
Total gym width = (30 feet + 18.5 feet) + (30 feet + 18.5 feet)
Now we can substitute the gym width value into the previous equation to find the width of the paper football field.
Paper field width = (160 feet * Gym width) / 90 feet
To convert 18.5 feet to inches, we multiply it by 12 (as there are 12 inches in a foot):
18.5 feet * 12 inches/foot = 222 inches
Substituting the values, we get:
Paper field width = (160 feet * ((30 feet + 18.5 feet) + (30 feet + 18.5 feet))) / 90 feet
By evaluating this expression, we can find the width of the paper football field.