On a centimeter dot grid, draw all possible rectangles with a perimeter of 14 cm and sides whose lengths are whole centimeters.
What's the area?
P = 2L + 2W
1 by 6
2 by 5
3 by 4
Why did the rectangle visit the therapist? Because it had too many sides but couldn't find a perfect match! Alright, let's draw those rectangles!
Here are all the possible rectangles with a perimeter of 14 cm on a centimeter dot grid:
1) Rectangle with sides 1 cm and 6 cm:
_______
| |
| U |
|_______|
2) Rectangle with sides 2 cm and 5 cm:
_______
| @ |
|__@____|
3) Rectangle with sides 3 cm and 4 cm:
_______
| @ @ |
|______|
4) Rectangle with sides 4 cm and 3 cm:
_______
| @ @ |
|______|
5) Rectangle with sides 5 cm and 2 cm:
_______
| @ |
| @ |
|______|
6) Rectangle with sides 6 cm and 1 cm:
_______
| U |
|_______|
So, there you have it! All the possible rectangles with a perimeter of 14 cm on a centimeter dot grid.
To find all possible rectangles with a perimeter of 14 cm and sides whose lengths are whole centimeters, we can start by listing all the possible combinations of side lengths.
Let's consider one side as the length and the other side as the width. The perimeter of a rectangle is given by the formula: P = 2(length + width). In this case, P = 14 cm. Since the lengths and widths are whole numbers, we can limit our search to the positive integers that add up to 7, because 14 cm divided by 2 is 7.
Here are the possible combinations:
1. Length = 1 cm and Width = 6 cm (1 + 6 = 7)
2. Length = 2 cm and Width = 5 cm (2 + 5 = 7)
3. Length = 3 cm and Width = 4 cm (3 + 4 = 7)
4. Length = 4 cm and Width = 3 cm (4 + 3 = 7)
5. Length = 5 cm and Width = 2 cm (5 + 2 = 7)
6. Length = 6 cm and Width = 1 cm (6 + 1 = 7)
Now we can draw these rectangles on a centimeter dot grid.
For each rectangle, start by marking the bottom-left corner of the rectangle. Then count the number of centimeter squares along the length (from left to right) and along the width (from bottom to top).
1. Rectangle with Length = 1 cm and Width = 6 cm:
Start at a point on the grid and count 1 cm to the right (length) and then count 6 cm upwards (width).
2. Rectangle with Length = 2 cm and Width = 5 cm:
Start at a point on the grid and count 2 cm to the right (length) and then count 5 cm upwards (width).
3. Rectangle with Length = 3 cm and Width = 4 cm:
Start at a point on the grid and count 3 cm to the right (length) and then count 4 cm upwards (width).
4. Rectangle with Length = 4 cm and Width = 3 cm:
Start at a point on the grid and count 4 cm to the right (length) and then count 3 cm upwards (width).
5. Rectangle with Length = 5 cm and Width = 2 cm:
Start at a point on the grid and count 5 cm to the right (length) and then count 2 cm upwards (width).
6. Rectangle with Length = 6 cm and Width = 1 cm:
Start at a point on the grid and count 6 cm to the right (length) and then count 1 cm upwards (width).
Repeat this process for each combination, and you will have drawn all possible rectangles with a perimeter of 14 cm and sides whose lengths are whole centimeters on the centimeter dot grid.