Coach Stevens needs to purchase sprinklers to water the baseball field. The standard distance between bases is 90 feet and the infield is a perfect square.

Coach Stevens found one sprinkler that sprays a maximum distance of 50 feet.

If Coach Stevens placed the sprinkler on the pitcher's mound, would the water spray so that the entire infield was watered? Justify your response.

Question

abdubasheer abdubasheer

10-10-2017
Mathematics

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Coach Stevens needs to purchase sprinklers to water the baseball field. The standard distance between bases is 90 feet and the infield is a perfect square.

Coach Stevens found one sprinkler that sprays a maximum distance of 50 feet.

If Coach Stevens placed the sprinkler on the pitcher's mound, would the water spray so that the entire infield was watered? Justify your response.

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mattmunoz0430 mattmunoz0430 · Answer 1 · 2021-01-29T18:44:58+01:00

Answer:

So, if coach Stevens places as sprinkler of maximum distance 50 ft, he won't be able to cover the entire infield.

Step-by-step explanation:

Consider the infield as a polygon ABCDE.

It is given that each side AB, BC, CD, and DA is of length 90ft. It is also given that the infield is a perfect square.

Thus, the area of the square ABCD = 8100 ft.

Now consider the triangle BCD. Because of symmetry, the area of this triangle equals half the area of the square. Again, because of symmetry, the length of the base BD equals twice the length of the height EC.

Thus from to the formula of area of the triangle:

base × height = 4050 base × height = 8100 2(height) × height= 8100 height63.64 ft