SOLUTION: Find the perimeter of a square that has diagonals 6 feet long.

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Question 352672: Find the perimeter of a square that has diagonals 6 feet long.
Found 2 solutions by ewatrrr, unlockmath:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
HI,
*Note: the 2 diagonals of a square are Of equal length. Diagonals form a right trangle with the length and width, with the diagonal being the hypotenuse.
.
Pythagorean Theorem gives the realtionship between the sides of a right triangle(sides meeting at a right angle) and its hypotenuse.
a%5E2+%2B+b%5E2+=+c%5E2
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Let x be the length of the each side of the square
x%5E2+%2B+x%5E2+=+6ft%5E2
.
2x%5E2+=+36ft%5E2
x%5E2+=+18ft%5E2
x+=+sqrt%2818ft%5E2%29+=+sqrt%289+%2A+2%29ft%5E2+=+3%2Asqrt%282%29+ft
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P+=+4%2A+3%2A+sqrt%282%29ft+=+12%2A+sqrt%282%29

Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
With this we can use the Pythagorus Formula to solve the sides.
Let x be the sides of the square so our equation will be:
x^2+x^2=6^2
Rewritten as:
2x^2=36
Divide by 2 to get:
x^2=18
Sq rt both sides to get:
x=sq rt 18
There we go. A side is sq rt 18 ft or approx 4.24 feet times 4 gives us a perimeter of 16.96 feet.
Make sense?
RJ
www.math-unlock.com