how many different rectanagles exist which have whole numbers as the length and width,and also have an area of 36sq.cm?
36
= 1x36
= 2x18
=3x12
=4x9
= 6x6
Factors of 36:
6 x 6
4 x 9
3 x 12
2 x 18
1 x 36
To find the different rectangles with whole numbers as the length and width, and an area of 36 sq. cm, follow these steps:
Step 1: Listing all possible factors of 36
- Start by listing all the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Step 2: Pairing the factors
- Pair up the factors to find the length and width combinations.
- For example, if the length is 1, the width will be 36 (1 x 36).
- If the length is 2, the width will be 18 (2 x 18).
- Continue this process with the remaining factors.
Step 3: Checking for duplicates
- Sometimes, the same pairs may be obtained but in reverse order. For example, if (1, 36) is a pair, then (36, 1) will be the same rectangle. In such cases, we count only one of them.
Step 4: Calculating the number of rectangles
- Count the number of rectangular combinations you obtain from the pairing process.
So, let's find the different rectangles:
1 x 36 (1 row, 36 columns)
2 x 18 (2 rows, 18 columns)
3 x 12 (3 rows, 12 columns)
4 x 9 (4 rows, 9 columns)
6 x 6 (6 rows, 6 columns)
9 x 4 (9 rows, 4 columns)
12 x 3 (12 rows, 3 columns)
18 x 2 (18 rows, 2 columns)
36 x 1 (36 rows, 1 column)
In total, there are 9 different rectangles.