SOLUTION: If the area of a square is 169 square centimeters, what is the length of the diagnal?

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Question 132521: If the area of a square is 169 square centimeters, what is the length of the diagnal?
Found 2 solutions by elima, solver91311:
Answer by elima(1433) About Me  (Show Source):
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If the area of a square is 169 square centimeters, what is the length of the diagnal?
formula for area of square;
a=s%5E2
169=s%5E2
take the square root of each side;
sqrt%28169%29=sqrt%28s%5E2%29
13=s
so the sides of the square are 13, now we can use Pythagoreans thereom to find the diagonal;
a%5E2+%2B+b%5E2+=+c%5E2
13%5E2+%2B+13%5E2+=+c%5E2
26%5E2+=+c%5E2
take square root of each side;
sqrt%2826%5E2%29+=+sqrt%28c%5E2%29
26 = c
so diagonal = 26
:)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a side of a square given the area is given by the square root of the area. So this square has a side length of sqrt%28169%29=13

The diagonal of any square forms an isoceles right triangle with two of the sides of the square, and the three sides of this triangle are in proportion 1:1:sqrt%282%29 (verify this yourself by considering an isoceles right triangle with legs that measure 1 unit, then applying the Pythagorean Theorem). Knowing that, all we need to do is multiply the side length times sqrt%282%29, in this case: 13sqrt%282%29 cm is the length of the diagonal of a square with an area of 169cm%5E2.