SOLUTION: what is the are of a square with a diagonal of 5?

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Question 35106: what is the are of a square with a diagonal of 5?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Being a square, the length of all sides is the same, call it x.

Draw a square and a diagonal. You create 2 right-angled triangles, so we can use Pythagoras' Theorem:

+a%5E2+%2B+b%5E2+=+c%5E2+ where length c is the hypotenuse, the longest side, here the diagonal of the square. So...

+x%5E2+%2B+x%5E2+=+5%5E2+
+2x%5E2+=+25+
+x%5E2+=+25%2F2+
+x+=+sqrt%2825%2F2%29+ taking just the positive version, since we are deaing with lengths of a square (lengths are not negative).

So, the area of a square is given by x%5E2, which from above is 25/2

jon.