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

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) (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

in this equation, x=a; a=1, b=-12, c=-36

we only want the positive solution here

a =
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 results: 20.5

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