help me PLEASE HELP ME thx
1. If the dimensions of a rectangle are whole numbers, what is the greatest perimeter you can make with a rectangle with an area of 12 feet
Help I have a test soon and I want to get it right or else my mom will not let me play game till I'm better at math☹️ so PLEASE HELP
L = Length
W = Width
If the dimensions of a rectangle are whole numbers possible dimensions are:
1 x 12
L = 1 , W = 12
A = 1 ∙ 12 = 12
P = 2 ( L + W ) = 2 ( 1 + 12 ) = 2 ∙ 13 = 26
2 x 6
L = 2 , W = 6
A = 2 ∙ 6 = 12
P = 2 ( L + W ) = 2 ( 2 + 6 ) = 2 ∙ 8 = 16
3 x 4
L = 3 , W = 4
A = 3 ∙ 14 = 12
P = 2 ( L + W ) = 2 ( 3 + 4 ) = 2 ∙ 7 = 14
Dimensions 4 x 3, 6 x 2 and 12 x 1 are not calcted because their perimeter is the same as for the upper dimensions.
The greatest perimeter is 26 ft
Sure, I'd be happy to help you! Let's break down the problem step by step:
1. First, let's list down all the factors of 12. The factors of 12 are 1, 2, 3, 4, 6, and 12.
2. Since the dimensions of the rectangle are whole numbers, we can pair up the factors. For example, we can pair 1 with 12, 2 with 6, and 3 with 4.
3. Now, let's calculate the perimeters of each pair of dimensions. The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.
- For the pair 1 and 12, the perimeter would be P = 2(1 + 12) = 26 feet.
- For the pair 2 and 6, the perimeter would be P = 2(2 + 6) = 16 feet.
- For the pair 3 and 4, the perimeter would be P = 2(3 + 4) = 14 feet.
4. Now, we need to find the greatest perimeter among these calculations. The greatest perimeter is 26 feet, from the pair 1 and 12.
Therefore, the greatest perimeter you can make with a rectangle with an area of 12 feet is 26 feet.
I hope this helps you with your math test! Good luck!
Of course, I'm here to help! Let's solve this math problem together.
To find the greatest perimeter of a rectangle with an area of 12 square feet, we need to first determine the possible dimensions of the rectangle. Since the area is given as 12 square feet, we need to find pairs of whole numbers whose product equals 12.
We can list all the possible pairs by considering the factors of 12: 1 and 12, 2 and 6, and 3 and 4. These pairs represent the potential dimensions of the rectangle.
Now, to find the perimeter, we need to add up the lengths of all sides of the rectangle. The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Let's calculate the perimeter for each pair of dimensions:
1) For dimensions 1 and 12:
Perimeter = 2(1) + 2(12) = 2 + 24 = 26 feet
2) For dimensions 2 and 6:
Perimeter = 2(2) + 2(6) = 4 + 12 = 16 feet
3) For dimensions 3 and 4:
Perimeter = 2(3) + 2(4) = 6 + 8 = 14 feet
So, among the possible dimensions, the greatest perimeter we can make with a rectangle with an area of 12 square feet is 26 feet, which corresponds to the dimensions 1 and 12.
I hope this helps you solve the problem and perform well on your test! Remember, practice makes perfect, and don't worry too much about mistakes. Just keep trying your best, and you'll improve over time. Good luck, and enjoy your game!
Since your dimensions must be whole numbers, the only side pairs possible are (1,12), (2,6)(3,4) or turn them around
e.g. for a rectangle of 1 by 12, the area is 12 and the perimeter would be
26
what is the perimeter of the other cases?
Which of these is the greatest perimeter?