Of all the rectangles with areas of 100 square units and with whole number side lengths, determine the dimensions of the rectangle with the greatest perimeter.
What is the least Perimeter
What is greatest perimeter?
the least will be one with side lengths that are closest to (or equal to) each other
the greatest will have side lengths that are farthest apart
so it would be 202 and 48
thanks
100 square units is a 10 x 10 square with a perimeter of 40
To determine the dimensions of the rectangle with the greatest perimeter, we need to consider all the possible rectangles with an area of 100 square units and whole number side lengths.
First, let's find all the possible pairs of whole numbers whose product equals 100:
1 x 100 = 100
2 x 50 = 100
4 x 25 = 100
5 x 20 = 100
10 x 10 = 100
For each pair, we can calculate the perimeter by adding up the lengths of all four sides. The formula for the perimeter of a rectangle is: P = 2(length + width).
For the given pairs, the perimeters are as follows:
1 x 100: P = 2(1 + 100) = 202
2 x 50: P = 2(2 + 50) = 104
4 x 25: P = 2(4 + 25) = 58
5 x 20: P = 2(5 + 20) = 50
10 x 10: P = 2(10 + 10) = 40
Therefore, the rectangle with dimensions 10 units by 10 units has the greatest perimeter, which is 40 units.
To determine the rectangle with the least perimeter, we can similarly calculate the perimeters for all the possible pairs mentioned earlier.
Among the given pairs, the rectangle with dimensions 5 units by 20 units has the least perimeter, which is 50 units.
So, the least perimeter is 50 units and the greatest perimeter is 40 units.