SOLUTION: Square MNOP has a diagonal of 12 inches. Find the length of each side of the square.

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Question 1132719: Square MNOP has a diagonal of 12 inches. Find the length of each side of the square.
Found 3 solutions by Boreal, MathLover1, Edwin McCravy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Square diagonals are the hypotenuse of a right triangle with two equal legs of length s
The diagonal is s sqrt(2), so if the diagonal is known and is d, the side is d/sqrt(2)
or d sqrt(2)/2
the side is 6 sqrt(2) inches.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Square MNOP+ has a diagonal of d=12in.
if the side of square is a, and diagonal cuts the square in two right triangles, using right triangle we have
d%5E2=a%5E2%2Ba%5E2
d%5E2=2a%5E2
a%5E2=d%5E2%2F2...........plug in d
a%5E2=%2812in%29%5E2%2F2
a%5E2=144in%5E2%2F2
a%5E2=72in%5E2
a=sqrt%2872in%5E2%29
a=6sqrt%282%29in-> exact solution-the length of each side of the square
a=8.49in%29->approximately



Answer by Edwin McCravy(20056) About Me  (Show Source):