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Q: Find the dimensions of the rectangle with an area of 100 square units and whole-number side lengths that has the largest perimeter or the smallest perimeter?

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It is 5 units * 20 units. A smaller perimeter can be attained by a square but the question specified a rectangle.

L + W >= 24, L = W + 4, Possible dimensions 14 and 10 giving an area of 140 sq cm.

405 inches

Information about the area is not enough to determine the perimeter. 640 acres is 1 sq mile. The smallest perimeter possible is if the area is in the shape of a circle and in that case the perimeter would be 3.54 miles = 18717 feet. If the area is a square the perimeter would be 4 miles = 21120 feet. If it is a rectangle, then any value greater than 4 miles.

There is no one answer, it depends on the shape. The smallest value of perimeter will be for a circle. For a four sided shape the smallest will be for a square, for a rectangle the perimeter gets bigger the longer and narrower the area becomes. Knowing the area in acres gives the number of square yards only, you have to know either the length or width, work out the width or length as the case may be, then just add up the four sides.

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There are almost infinite possibilities as you get smaller and smaller

The dimensions of the rectangle will then work out as 14 cm by 10 cm because the perimeter is 14+10+14+10 = 48 cm

It is 5 units * 20 units. A smaller perimeter can be attained by a square but the question specified a rectangle.

7 x 19 cm

40

The smallest is just over 40 units. At 40 units it is no longer a rectangle but a square. There is no largest perimeter.

The smallest perimeter is 4*sqrt(24) = approx 19.6 cm There is no largest perimeter.

square

A square.

Largest = 86, Smallest 26

L + W >= 24, L = W + 4, Possible dimensions 14 and 10 giving an area of 140 sq cm.

16 and 12

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