SOLUTION: Two sides of a rectangle are parallel to each other and are doneted as y. The other two sides of the rectangle are also parallel to each other and are denoted as x. If the sides x

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Question 709295: Two sides of a rectangle are parallel to each other and are doneted as y. The other two sides of the rectangle are also parallel to each other and are denoted as x. If the sides x of the rectangle are increased by 3 units, the resulting figure is a square with area 20. What was the original area?

My attempt: y(x+3)=20
y=x+3
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The original area is A = xy

The new area is y(x+3) = xy + 3y and this is equal to 20, so

xy + 3y = 20

We know that the new figure is a square, so y = x+3

Plug this in and solve for x

xy + 3y = 20

x(x+3) + 3(x+3) = 20

x^2 + 3x + 3x + 9 = 20

x^2 + 6x + 9 - 20 = 0

x^2 + 6x - 11 = 0

Now use the quadratic formula to solve for x


x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%286%29%2B-sqrt%28%286%29%5E2-4%281%29%28-11%29%29%29%2F%282%281%29%29 Plug in a+=+1, b+=+6, c+=+-11

x+=+%28-6%2B-sqrt%2836-%28-44%29%29%29%2F%282%29

x+=+%28-6%2B-sqrt%2836%2B44%29%29%2F%282%29

x+=+%28-6%2B-sqrt%2880%29%29%2F2

x+=+%28-6%2Bsqrt%2880%29%29%2F2 or x+=+%28-6-sqrt%2880%29%29%2F2

x+=+%28-6%2B4%2Asqrt%285%29%29%2F2 or x+=+%28-6-4%2Asqrt%285%29%29%2F2

x+=+-3%2B2%2Asqrt%285%29 or x+=+-3-2%2Asqrt%285%29

x+=+1.472136 or x+=+-7.472136

Note: Solutions above are approximate

Ignore the negative solution

So x is roughly 1.472136 and y = x+3 = 1.472136+3 = 4.472136

So x = 1.472136 and y = 4.472136


The area of the original rectangle is therefore

A = xy

A = 1.472136*4.472136

A = 6.583592402496

So the area of the original rectangle is roughly 6.583592402496 square units.

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
You seem about half way there.
y(x+3)=20. Substitute!...
(x+3)(x+3)=20. Both sides became the same size when the x was lengthened, which is why you equated y and x+3. The y was not changed but now matches the length of the other direction.
x%5E2%2B6x%2B9-20=0
x%5E2%2B6x-11=0

x=(-6+- sqrt(36-4*(-11)))/2
(-6+- sqrt(80))/2
(-6+-4sqrt(5))/2
-3+-2sqrt(5)
The negative not reasonable, so
x=-3%2B2sqrt%285%29

y=x+3
y=-3+2sqrt(5)+3
y=2sqrt%285%29

Original Area, highlight%28xy=%28-3%2B2sqrt%285%29%29%282sqrt%285%29%29%29