SOLUTION: Wondering if I am on the right track. I need to determine a quadratic equation to solve the problem and also solve the problem. My word question is as follows: The perimeter of

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Question 206251: Wondering if I am on the right track. I need to determine a quadratic equation to solve the problem and also solve the problem. My word question is as follows: The perimeter of a rectangle is 34 cm and the diagonal is 13 cm. Determine the lengths of the side of the rectangle.
I am setting up my equation as follows:
2x + 2y = 34
x^2 + y^2 = 169
I then determine (x) by the following equation:
2x + 2y = 34
2x = 34 - 2y
x = 17 - y
Then I am taking the following equation to come up with a quadratic equation:
(17-y)^2 + y^2 = 169
189 - 34y + y^2 + y^2 = 169
2y^2 - 34y = -20
2y^2 - 34y + 20 = 0
Then my final answer (?) after calculating the quadratic equation is:
x = 34 + or - 498 / 4
x = 133 and x = 116
My question is, am I doing this correctly or am I missing a step?
Your input would be greatly appreciated.
Lori
Found 2 solutions by Targetweek, mickclns:
Answer by Targetweek(62) About Me  (Show Source):
You can put this solution on YOUR website!
Yes you are doing it correctly but you messed up when you tried to solve the quadratic equation because...
- 17-y%29%5E2+%2B+y%5E2+=+169
- highlight%28289%29+-+34y+%2B+y%5E2+%2B+y%5E2+=+169
- 17%5E2+=+289 , 17%5E2+%3C%3E+189
So besides that you did it right but i'll go ahead and finish it for you
- 289+-+34y+%2B+2y%5E2+=+169
- 2y%5E2+-+34y+%2B+289+-+169+=+169-169
- 2y%5E2+-+34y+%2B+120+=+0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-34x%2B120+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-34%29%5E2-4%2A2%2A120=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--34%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-34%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+12
x%5B2%5D+=+%28-%28-34%29-sqrt%28+196+%29%29%2F2%5C2+=+5

Quadratic expression 2x%5E2%2B-34x%2B120 can be factored:
2x%5E2%2B-34x%2B120+=+2%28x-12%29%2A%28x-5%29
Again, the answer is: 12, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-34%2Ax%2B120+%29

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Since your solutions for x are 12 and 5, the side lengths are 12 and 5 because you get the same answer if x=12,y=5 as x=5,y=12
hope that helped!

Answer by mickclns(59) About Me  (Show Source):
You can put this solution on YOUR website!
Lori, you definitely are on the right track. The first mistake came when you squared 17 and got 189; it should be 289.
Also, when you use the quad. eqn. you should have (-b +/- SQRT(...) ) / 2a
Don't forget the square root and don't forget the parens ... when you write a fraction horizontally, you need parens around the numerator of the fraction if you are adding or subtracting ... the horizontal line in the fraction acts as a grouping operator, so that needs to be replaced by parens.
Be careful on your calculations, too, don't do it in your head (I know, you probably did it on a sheet of paper and typed the answer into the computer. I say this because the 498 is not correct either).
It's good you asked for proofreading your work rather than saying "how do you do it?" because you learn more the more you do it yourself. Just try it again and be a little more careful.