SOLUTION: Pythagorean Theorem The diagonals of a square bisect each other at right angles. What is the length of a side of a square if the diagonals are each 12 inches long?

Algebra ->  Equations -> SOLUTION: Pythagorean Theorem The diagonals of a square bisect each other at right angles. What is the length of a side of a square if the diagonals are each 12 inches long?      Log On


   

Question 388290: Pythagorean Theorem
The diagonals of a square bisect each other at right angles. What is the length of a side of a square if the diagonals are each 12 inches long?
Answer by nerdybill(7384) About Me  (Show Source):
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The diagonals of a square bisect each other at right angles. What is the length of a side of a square if the diagonals are each 12 inches long?
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Applying Pythagorean theorem:
Let x = length of one side of the square
then
+x%5E2+%2B+x%5E2+=+12%5E2+
+2x%5E2+=+12%5E2+
+2x%5E2+=+144+
+x%5E2+=+72+
+x+=+sqrt%2872%29+
+x+=+sqrt%286%2A6%2A2%29+
+x+=+6%2Asqrt%282%29+ inches
or, decimal approximation:
+x+=+8.49+ inches