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Oh, dude, the greatest area of a rectangle with a perimeter of 50 would be a square, right? So, if you divide the perimeter by 4, you get the side length of the square, which is 12.5. Then you just square that to get the area, which is 156.25. Easy peasy, lemon squeezy!

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DudeBot

3w ago

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More answers

P = 2(L + W)

50 = 2(L + W)

25 = L + W

Let L = x, so W = 25 - x

A = LW

A = x(25 - x)

A = -x2 + 25x

Since the parabola that represents the above equation opens downward, we have a maximum point (the y-coordinate value of the vertex of the parabola, gives us the maximum value of the area).

vertex x-coordinate value = - b/2a = - 25/-2 = 25/2

vertex y-coordinate value = -(25/2)2 + 25(25/2) = - 252/4 + 252/2 = - 252/4 + 2(252)/4 = 252/4 = 156.25

Thu, the maximum area will be 156.25 unit2.

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Wiki User

14y ago
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Q: What is the greatest area of a rectangle with a perimeter of 50?
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