For the given perimeter, find the length and width of the rectangle with
the greatest area Use whole numbers only.
60yd
54cm
To find the dimensions of the rectangle with the greatest area for a given perimeter, you can use the concept of maximizing the area by finding the square or a rectangle that is closer to a square.
For a rectangle, the perimeter (P) is given by the formula:
P = 2 * (length + width)
Given a perimeter of 60 yards (60yd), we have the equation:
60 = 2 * (length + width)
Now, we need to find the length and width that satisfy this equation. We have to keep in mind that we can only use whole numbers.
To simplify the equation, let's divide both sides by 2:
30 = length + width
Now, we need to find the combination of length and width that sums up to 30. We want to maximize the area, so we should search for numbers that are close to each other. One possible combination could be:
length = 15
width = 15
Let's calculate the area of this rectangle:
Area = length * width
Area = 15 * 15
Area = 225 square yards
So, for a perimeter of 60 yards, the rectangle with dimensions 15 yards by 15 yards would have the greatest area, which is 225 square yards.
Now, let's do the same for the given perimeter of 54 cm:
54 = 2 * (length + width)
Divide by 2:
27 = length + width
Again, we need to find whole numbers that add up to 27 to maximize the area. Let's try:
length = 13
width = 14
Calculating the area:
Area = length * width
Area = 13 * 14
Area = 182 square centimeters
For a perimeter of 54 centimeters, the rectangle with dimensions 13 centimeters by 14 centimeters would have the greatest area, which is 182 square centimeters.