SOLUTION: I have a word problem on a sheet that I don't really understand. I would really love to know the steps to solving it since there are more of them. I've tried the pythagorean theore

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Question 566135: I have a word problem on a sheet that I don't really understand. I would really love to know the steps to solving it since there are more of them. I've tried the pythagorean theorem, but I don't think I'm doing it right. I would greatly appreciate any help I receive.
In a square, the length of a side is 6 cm less than a diagonal. How long is each diagonal?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In a square, the length of a side is 6 cm less than a diagonal.
How long is each diagonal?
:
Let c = the diagonal
then
a = the side of the square
then
c = (a+6)
:
Using pythag: a^2 + b^2 = c^2, (you're right about that!)
It's a square so a = b, so we can write it
2a^2 = (a+6)^2
FOIL (a+6)(a+6)
2a^2 = a^2 + 6a + 6a + 36
2a^2 = a^2 + 12a + 36
Combine like terms on the left
2a^2 - a^2 - 12a - 36 = 0
a^2 - 12a - 36 = 0
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this equation, x=a; a=1, b=-12, c=-36
a+=+%28-%28-12%29+%2B-+sqrt%28-12%5E2-4%2A1%2A-36+%29%29%2F%282%2A1%29+
:
a+=+%2812+%2B-+sqrt%28144-%28-144%29+%29%29%2F2+
:
a+=+%2812+%2B-+sqrt%28288+%29%29%2F2+
we only want the positive solution here
a+=+%2812+%2B+16.97%29%2F2+
a = 28.97%2F2
a = 14.5 cm is the length of the side
but they want the diagonal
14.5 + 6 = 20.5 cm is the length of the diagonal
;
:
Check this on your calc: enter sqrt%2814.5%5E2+%2B+14.5%5E2%29 results: 20.5