A rope 100 feet long is stretched around four posts set at the corners of a rectangle whose area is 576 square feet. Find the dimensions of the rectangle.

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- Dec 6th 2008, 07:16 AMmagentaritaDimensions of Rectangle
A rope 100 feet long is stretched around four posts set at the corners of a rectangle whose area is 576 square feet. Find the dimensions of the rectangle.

- Dec 6th 2008, 07:24 AMjanvdl
Since the rope is 100 feet long, then the perimeter of this rectangle must be 100 feet long too.

So we can say:

$\displaystyle P = 100 = 2L + 2W$

And simplify that to:

$\displaystyle 50 = L + W$

And let's rearrange that to:

$\displaystyle L = 50 - W$

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Now let's go to the area (This is going to end up as a simul. equation)

$\displaystyle A = 576 = LW$

Now let's substitute that value we have for the length

$\displaystyle 576 = (50 - W)(W)$

$\displaystyle 576 = 50W - W^2$

$\displaystyle W^2 - 50W + 576 = 0$

Solve for W, and subsequently L. - Dec 7th 2008, 09:03 AMmagentaritaok.....