How do you find the dimensions of a rectangle with area 1000 m whose perimeter is as small as possible?

Answer 1

Actually I found equal dimensions of #31.62m#, i.e., a square...check my method and maths!

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Answer 2

To find the dimensions of a rectangle with an area of 1000 m² and a perimeter as small as possible, you need to use optimization techniques. Let ( x ) and ( y ) represent the length and width of the rectangle, respectively. Since the area is given by ( A = xy ) and the perimeter is given by ( P = 2x + 2y ), we have the equations ( xy = 1000 ) and ( P = 2x + 2y ). To minimize the perimeter, we can use the first equation to express one variable in terms of the other, substitute it into the perimeter equation, and then differentiate the resulting equation with respect to one variable and solve for that variable. By doing this, we find that the dimensions of the rectangle with the smallest perimeter are approximately ( x \approx 25.1 ) m and ( y \approx 39.7 ) m.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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