Verified Answer :

Step-by-step explanation:

Given : 24 square pieces of wood

Taking L.C.M of 24.

\(24=2\times 2\times 2\times 3\times 1\)

1) \(24=4\times 6\)

By placing 4 square pieces in row and 6 square pieces in column we would be able to make rectangle

2) \(24=8\times 3\)

By placing 8 square pieces in row and 3 square pieces in column we would be able to make rectangle

3)\(24=12\times 2\)

By placing 12 square pieces in row and 2 square pieces in column we would be able to make rectangle

4)\(24=24\times 1\)

By placing 24 square pieces in row and 1 square pieces in column we would be able to make rectangle

5) \(24=6\times 4\)

By placing 6 square pieces in row and 4 square pieces in column we would be able to make rectangle

6) \(24=3\times 8\)

By placing 3 square pieces in row and 8 square pieces in column we would be able to make rectangle

7)\(24=2\times 12\)

By placing 2 square pieces in row and 12 square pieces in column we would be able to make rectangle

8)\(24=1\times 24\)

By placing 1 square pieces in row and 24 square pieces in column we would be able to make rectangle

Answer:

The possible dimensions of rectangles are 1×24, 2×12, 3×8, 4×6, 6×4, 8×3, 12×2, 24×1.

Explanation:


Factors: If two or more numbers are multiplied together to get a new number, then those numbers are called factors of that new number.


Factor pairs: If two numbers are multiplied to get a new number, then those numbers are called factor pairs of that new number. For example: Factor pairs of 6 are (1,6) and  (2,3).

Further Explanation:


It is given that  24 square pieces of wood.

We need to find all the different ways you could make a rectangle by placing them side-by-side.

Find the factors of 24.

\(24=1\times 2\times 2\times 2\times 3\)

Now find factor pairs of 24.

  • \(24=1\times 24\)
  • \(24=2\times 12\)
  • \(24=3\times 8\)
  • \(24=4\times 6\)

So, the factor pairs of 24 are (1,24), (2,12), (3,8) and (4,6).

Here, (1,24) means 1 square pieces in row and 24 square pieces in column and (24, 1) means 24 square pieces in row and 1 square pieces in column. So, the other possible dimensions are (24,1), (12,2), (8,3) and (6,4).

 

Factor pair               square pieces in row            square pieces in column

    (1,24)                                    1                                        24

    (2,12)                                    2                                        12

    (3,8)                                      3                                        8

    (4,6)                                      4                                        6

   (24,1)                                     24                                       1

   (12,2)                                     12                                        2

   (8,3)                                        8                                        3

   (6,4)                                        6                                        4

Learn More:

For factor pairs : https://brainly.com/question/696109 (Answered by Calculista)

For factors and factor pairs :https://brainly.com/question/744701  (Answered by DelcieRiveria)

Keywords:

Factors of a number, factor pairs

Related Questions