SOLUTION: A Little Leaguer asks her mother to make her a home plate for a sandlot baseball game. According to her encyclopedia, an official plate is made from a square by making two 12-inch

Algebra ->  Length-and-distance -> SOLUTION: A Little Leaguer asks her mother to make her a home plate for a sandlot baseball game. According to her encyclopedia, an official plate is made from a square by making two 12-inch       Log On


   

Question 1008122: A Little Leaguer asks her mother to make her a home plate for a sandlot baseball game. According to her encyclopedia, an official plate is made from a square by making two 12-inch diagonal cuts that remove isosceles triangles. What is the length of the side of the original square?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
C=length of diagonal, A=B=lengths of sides:
A%5E2%2BB%5E2=C%5E2 Pythagorean theorem
A%5E2%2BA%5E2=C%5E2
2A%5E2=C%5E2
2A%5E2=%2812in%29%5E2
2A%5E2=144in%5E2
A%5E2=72in%5E2
sqrt%28A%5E2%29=sqrt%2872in%5E2%29
A=8.485
Since the two diagonals meet at the back center of
the original square, the side of the square
is 2 times the length of the sides of the triangle:
Side of square=2A
Side of square=2(8.485)
Side of square=16.97 inches
The player's "Encyclopedia" is wrong:
The official rules call for a square 17 inches with
diagonals that meet in the back center starting 8.5 inches
from the front of the plate. The sides of the triangles
would be 8.5 inches, making the diagonal:
sqrt%282%288.5%5E2%29%29=12.02in
or 12.02 inches, not 12 inches