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the numbers on the football field indicate 10 yards increments. you walk around the perimeter of the football field between the pylons. you walk a distance of 306 2/3. find the perimeter of one end zone

User JuanDM
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2 Answers

7 votes

The perimeter of one end zone is 126.67 yards.

To calculate this, we first need to know the total perimeter of the football field. The numbers on the field indicate 10-yard increments, so we can count 10 yards between each pair of pylons. There are 10 pairs of pylons on the field, so the total perimeter of the field is 10 * 10 = 100 yards.

The football field is 120 yards long, including the end zones. This means that each end zone is 10 yards long. Therefore, the perimeter of one end zone is 2 * 10 = 20 yards.

However, the end zones are not straight lines. They are curved, with a radius of 10 yards. This means that the perimeter of one end zone is not just 20 yards. We need to use the formula for the circumference of a circle to find the perimeter of the curved part of the end zone.

The formula for the circumference of a circle is C = 2πr, where C is the circumference, r is the radius, and π is a mathematical constant approximately equal to 3.14159.

Plugging in the values for the radius of the end zone, we get C = 2π(10) ≈ 62.83 yards.

Therefore, the perimeter of one end zone is 20 + 62.83 = 82.83 yards.

the numbers on the football field indicate 10 yards increments. you walk around the-example-1
User Garis M Suero
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6 votes

Answer:

Perimeter of one end zone = 126.66 yards.

Explanation:

Perimeter of the football field between the pylons = Perimeter of ABCD in the figure =
306(2)/(3)

Now in figure we can see, If we remove the length of line segment AB and CD, we will left with sides of end zones AD and BC.

AD + BC = 306.67 - 200 ( each increment by 10 , therefore 10 x 10 + 10 x 10 = 200) = 106.67 yards

In figure, we can see AD = PQ = BC = half of 106.67 yards

So, PQ + AD = 106.67

Now, For one end zone which is of triangular shape, Perimeter = PQ + AD + AP + QD = 106.67 + 10 + 10 = 126.67 yards

Note:- In figure, we can see AP = QD = 10 (∵ increment by 10 yards)

Thus, the perimeter of one end zone is 126.67 yards.

the numbers on the football field indicate 10 yards increments. you walk around the-example-1
User Tierra
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