The area of the rectangle below is 56 cm2.
Which of the following are possible values for the length and width of the rectangle?
There's infinite possibilities. If you're looking for integer values for the length and width, here are some:
L * W
1 * 56
2 * 28
4 * 14
7 * 8
8 * 7
14 * 4
28 * 2
56 * 1
To find the possible values for the length and width of the rectangle, we can factorize the area of the rectangle, which is 56 cm².
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, and 56.
We can pair up these factors to find possible values for the length and width of the rectangle:
Pair 1: Length = 1 cm, Width = 56 cm
Pair 2: Length = 2 cm, Width = 28 cm
Pair 3: Length = 4 cm, Width = 14 cm
Pair 4: Length = 7 cm, Width = 8 cm
Therefore, the possible values for the length and width of the rectangle are:
1 cm by 56 cm
2 cm by 28 cm
4 cm by 14 cm
7 cm by 8 cm
To find the possible values for the length and width of the rectangle, we need to consider the factors of the area given. The area of a rectangle is calculated by multiplying its length and width together.
Given that the area of the rectangle is 56 cm2, we need to find pairs of factors whose product equals 56.
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, and 56.
Now, we can test each pair of factors to see if they form a valid length and width for the rectangle. For example, if we take the first pair, 1 and 56, and use them as the length and width, we can calculate the area as follows.
Area = length × width
Area = 1 cm × 56 cm
Area = 56 cm2
This confirms that the pair (1, 56) is a valid combination for the length and width of the rectangle.
Similarly, we can test the other pairs of factors to determine all the possible values. After testing each pair, we find the following combinations that yield an area of 56 cm2:
- Length: 1 cm, Width: 56 cm
- Length: 2 cm, Width: 28 cm
- Length: 4 cm, Width: 14 cm
- Length: 7 cm, Width: 8 cm
Therefore, the possible values for the length and width of the rectangle are (1 cm, 56 cm), (2 cm, 28 cm), (4 cm, 14 cm), and (7 cm, 8 cm).