What is the greatest perimeter of a rectangle with an area of 39 square feet?
ROux
To find the greatest perimeter of a rectangle with a given area, we need to consider that rectangles with the same area can have different perimeters depending on the dimensions.
Let's first find the possible dimensions of the rectangle with an area of 39 square feet. To do this, we can factorize 39 into two numbers, as the dimensions of a rectangle are usually expressed as length and width.
Factorizing 39, we have:
1 × 39
3 × 13
So, the possible dimensions of the rectangle are 1 ft × 39 ft or 3 ft × 13 ft.
To find the perimeters corresponding to these dimensions, we can use the formula for perimeter:
Perimeter = 2 × (Length + Width)
For the first set of dimensions (1 ft × 39 ft):
Perimeter = 2 × (1 + 39) = 2 × 40 = 80 ft
For the second set of dimensions (3 ft × 13 ft):
Perimeter = 2 × (3 + 13) = 2 × 16 = 32 ft
Thus, the greatest perimeter of a rectangle with an area of 39 square feet is 80 feet.
I think you got it backwards. You want the minimium perimeter, not the max
e.g. I could have a rectangle of .05 ft by 780 ft, with a perimeter of 156.01 ft
I can make the width smaller and smaller and the perimeter would get bigger and bigger
for the smallest perimeter, the rectangle should be a square and its perimeter is
4√39 = ..... ft