Impossible Rectangle

Is it possible for a rectangle with a 48 cm perimeter to have an area of 150 square cm? Explain.

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The maximum possible area for a given perimeter occurs when the rectangle is a square.

If the perimeter is 48 cm, each side of the square is 12 cm, and the area would be only 144 square cm.

So it’s not possible for the rectangle to have an area of 150 square cm.

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