SOLUTION: Can you please explain to me how you find the answer to this problem: If two parallel sides of a square are increased by 6 cm and the other two parallel sides are each decreased by

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can you please explain to me how you find the answer to this problem: If two parallel sides of a square are increased by 6 cm and the other two parallel sides are each decreased by      Log On


   

Question 856: Can you please explain to me how you find the answer to this problem: If two parallel sides of a square are increased by 6 cm and the other two parallel sides are each decreased by 1 cm, a rectangle is formed having twice the area of the square. How long was each side of the square?
Answer by usyim88hk(158) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of one side of the square be x:
+x%5E2+ is the area of the square
Area of the retangle:
(x+6)(x-1)
which is equal to
+x%5E2%2B5x-6+
so if the area of the retangle is twice the area of the square, then we can set up an equation:
+x%5E2%2B5x-6=2x%5E2+
Now, slove it:
+x%5E2%2B5x-6-x%5E2=2x%5E2-x%5E2+
+5x-6=x%5E2+
+5x-6-x%5E2=x%5E2-x%5E2+
+-x%5E2%2B5x-6=0+
Now use the quadratic formula to slove:
x+=+%28%28-5%29+%2B-+sqrt%28%28-5%5E2%29-4%2A%28-1%29%2A%28-6%29%29%2F%282%2A%28-1%29%29%29
x+=+%28%28%28-5%29+%2B-+sqrt%28%2825-24%29%29%29%2F%28-2%29%29
x+=+%28%28%28-5%29%2B-+1%29%2F%28-2%29%29
x = (-4/-2) or (-6/-2)
x = 2 or 3
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Check:
if x=2
x^2 = 4
(2+6)(2-1) = 8
8 = 2*4
8=8 (2 is right!)
if x=3
x^2 = 9
(3+6)(3-1) = 18
18 = 2*9
18=18 (3 is right!)
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So the answer is 2 or 3, they both work!