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A rectangle has a perimeter of 60 inches. What dimensions would maximize the area.

User Kasturi
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1 Answer

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Answer: 15x15

Explanation:

I'm assuming this is an optimization problem in a Calculus class, if not just disregard all of this and be happy with the answer.

We can write two equations for the value of x and y lengths of this rectangle.

2y+2x=60

xy=A

Solve our perimeter equation for y, y=30-x.

This gives us x(30-x)=A, and 30x-x²=A.

Find the derivative of the area function: A'=30-2x

To maximize we set A' to 0: 0=30-2x, x=15

Plug back into our perimeter formula: 2y+2(15)=60, y=15

So both sides will be 15 inches.

User YonahW
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