High School

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Solar panels use the sun's energy to generate power. A town wants to install 28 solar panels in an array. What are all the possible ways the panels could be installed?

Answer :

Answer:

The possible arrays are: (1,28) , (2,14) , (4,7)) , (7,4) , (14,2) and (28,1)

Step-by-step explanation:

Here, the total number of solar panels to be installed = 28

Let us assume the installed array has m rows and n columns.

Now, the total panels installed = Number of rows x Number of columns

or, 28 = m n

The following cases are possible for array:

(a) When m = 1, n = 28 (as m x n = 28)

So, here array has 1 row with 28 columns.

(b) When m = 2, n = 14 (as m x n = 28)

So, here array has 2 row with 14 columns.

(c) When m = 4, n = 7 (as m x n = 28)

So, here array has 4 row with 7 columns.

(d) When m = 7, n = 4 (as m x n = 28)

So, here array has 7 row with 4 columns.

(e) When m = 14, n = 2 (as m x n = 28)

So, here array has 14 row with 2 columns.

(f) When m = 28, n = 1 (as m x n = 28)

So, here array has 28 row with 1 columns.

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Rewritten by : Barada

Final answer:

To determine the possible arrays for 28 solar panels, we look for factor pairs of 28. The configurations include 1x28, 2x14, 4x7, and 7x4 arrays.

Explanation:

The question is asking about the different ways a set of 28 solar panels can be arranged into an array. When arranging items into rows and columns, we look for pairs of factors that can multiply together to give the total number of items—in this case, 28. The factors of 28 are pairs of numbers that multiply together to make 28. These factors are: 1 & 28, 2 & 14, 4 & 7. Therefore, there are four main possible arrangements for the solar panels:

  • 1 row of 28 solar panels
  • 2 rows of 14 solar panels
  • 4 rows of 7 solar panels
  • 7 rows of 4 solar panels

Each configuration could be considered a valid array, depending on the physical space available and the design preferences for the installation.