SOLUTION: The distance from first to second base in indoor baseball is 33ft less than the corresponding distance in softball. The square bounded by the bases of an indoor baseball diamond is

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Question 71313: The distance from first to second base in indoor baseball is 33ft less than the corresponding distance in softball. The square bounded by the bases of an indoor baseball diamond is 2871 square feet less in area than that bounded by the bases of a softball diamond. Find the distance from one base to the other in indoor baseball.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The distance from first to second base in indoor baseball is 33 ft less than the corresponding distance in softball. The square bounded by the bases of an indoor baseball diamond is 2871 square feet less in area than that bounded by the bases of a softball diamond. Find the distance from one base to the other in indoor baseball.
:
Let x = base distance on an indoor baseball field
:
x^2 = the area of an indoor baseball field
:
(x+33) = base distance on a softball field
:
(x+33)^2 = area of a softball field
:
Problem states:
Softball field area - 2871 = indoor field area
(x+33)^2 - 2781 = x^2
x^2 + 66x + 1089 - 2871 = x^2: FOILed (x+33)(x+33)
x^2 + 66x - 1782 = x^2
x^2 - x^2 + 66x - 1782 = 0; subtracted x^2 from both sides
66x - 1782 = 0
66x = +1782
x = 1782/66
x = 27 ft, base distance, indoor baseball
:
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Check solution: Softball dist = 27+33 = 60: 60^2 - 27^2 = 2871