Question

A rectangle is divided into 12 columns and 6 rows, making 72 smaller rectangles. An area that includes 9 smaller rectangles and is the intersection of 3 of the 12 columns and 3 of the 6 rows is shaded.(1 point)
Responses

312×36

3 12 × 3 6

310×12

3 10 × 1 2

14×12

1 4 × 1 2

14×13

1 4 × 1 3

412×36

Answer 1

To find the dimensions of the shaded area that includes 9 smaller rectangles, we start by identifying how the smaller rectangles are arranged within the larger rectangle.

Given:
- The rectangle is divided into 12 columns and 6 rows.
- Each smaller rectangle represents one column and one row, giving a total of \(12 \times 6 = 72\) smaller rectangles.

The shaded area consists of 3 of the 12 columns and 3 of the 6 rows. The number of smaller rectangles in the shaded area is:

\[
3 \text{ (columns)} \times 3 \text{ (rows)} = 9 \text{ smaller rectangles}
\]

To find the dimensions of the entire shaded rectangle, we also need to know the dimensions of each smaller rectangle. Since we don't have specific numerical dimensions given directly in the problem, we'll use given multiple-choice responses to determine the proper dimensions.

The options for the dimensions of the shaded area based on the format provided in the responses include:

- \(3 \frac{12}{13}\)
- \(3 \frac{10}{12}\)
- \(14 \times 12\)
- \(14 \times 13\)
- \(4 \frac{12}{36}\)

### Analyzing options

The essential characteristic of the shaded area is that it is formed by taking 3 columns and 3 rows. The possible dimensions should relate to this structure, giving us the dimensions of the shaded rectangle \(3\) columns (width) and \(3\) rows (height).

Looking at the format of the options:
1. \(3 \frac{12}{36}\) - This option reads as a confusing fraction not related to height or width that meets the area described.
2. The conversion implies \(3 \text{columns} \times 3 \text{rows}\).

### Choosing the right option

Among the listed options, "3 \( \frac{10}{12} \)" seems to be the only fraction that relates to the structural proportion of width by height without offering irrational calculations not associated with the basic dimensions \(3 x 3\).

Thus, the appropriate inferred dimensions for the shaded area that includes 9 smaller rectangles based on the columns and rows is:

\[
3 \times 3
\]

Therefore, the final answer identifying such is:

\[
3 \times 3
\]

Thus, opting for the integer-scalable version of \(3 \) discerned correctly among choices would warrant a 3 through normalization; nevertheless, due to no pure original dimensions being represented numerically, it would validate more toward practical inference across design representations seen.

**Final Answer: 3 columns and 3 rows comprise the shaded area yielding dimensions accordingly within 3x3 roles from total layout.**