This can not be right -- baseball home plate!
This problem's question: What is the mathematical error in the specifications for a baseball home plate! "
The problem's answer is implicitly among the supplied answer. The correct choice is the best of the supplied answers.
You do not have to understand how to play baseball to answer this question.
The shape of home plate is the the only matter of concern in this problem. The shape of home plate is stated in the rules for the playing field as: "Front edge 17 inches wide; sides are parallel to the inside lines of batter’s boxes and are 8 ½ inches long; sides of the point facing the catcher are 12 inches long."
See Layout at Home Plate, 1st, 2nd, and 3rd Bases , page 155.
Since the four base lines are equilateral (90 feet) and right angles are specified at the other three corners, the home base angle is also a right angle. The axis line between the intersections of the base lines from first and third base to home base and second base provides additional angles.
The front edge is at the top in the image below. The rules implicitly specify that front edge of home plate be perpendicular to the axis line. The angles to the vertical sides from the front edge are right angles by requiring the vertical sides to be parallel to the sides of the batter boxes which are required to be parallel to the axis line. The angle where the 12 inch sides of the lower portion isosceles triangle meet at the apex of home plate is implicitly specified by the requirement that the 12 inch sides are on the base lines to first and third base.
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1 solution
1 7 2 = 1 2 2 + 1 2 2 . Pythagoras would be surprised! The batter box sides are specified as being parallel and perpendicular to a line from the apex of the home plate and the intersection of the baselines from first and third base to second base (the base furthest from home base).
Re metric, American rules, American measurements. Yes, metric is legal for commercial use in the United States. Baseball uses the also legal Imperial measure.
Re specifications, the specifications are directly out of the rule book. By definition the rule book is the specifications.
Re baseball diamond is not square, again directly from the specifications.
You do not need to know the relationship of feet and inches to solve this problem. The baselines are measured in feet. The home plate dimensions are all in inches. The ratio is 12 inches to 1 foot. For the curious, the current relationship is 0.0254 meters is 1 inch.