Use the image to answer the question.

A rectangle is divided into three sections. The first section has a length of 6 and a width of 15, the second has a length of x and a width of 15, and the third has a length of 4 and a width of 15. Each section is made up of multiple square boxes. The first is a 3 by 4 matrix of squares, the second is a 5 by 4 matrix of squares, and the third is a 2 by 4 matrix of squares. The common number 4 represents the width. Above the rectangle it reads: upper A equals 300 feet.

A farmer has a rectangular plot of land with an area of 300 square feet as shown in the diagram. Identify the equation to calculate the missing length based on the diagram shown.

(1 point)
Responses

15(x+10)=300
15 Left Parenthesis x plus 10 Right Parenthesis equals 300

15(6)+x+15(4)=300
15 Left Parenthesis 6 Right Parenthesis plus x plus 15 Left Parenthesis 4 Right Parenthesis equals 300

15(6+x)=300
15 Left Parenthesis 6 plus x Right Parenthesis equals 300

15x=300

1 answer

To find the missing length \( x \) in the diagram described, we first note that the total area of the rectangle is given as 300 square feet, and the width of each section is consistently stated as 15.

The area of a rectangle is calculated with the formula:

\[ \text{Area} = \text{Length} \times \text{Width} \]

In this case, the total area can be represented as the sum of the areas of the three sections together. The lengths of the first and third sections are provided, while the second section has an unknown length \( x \).

The equation representing the total area in terms of the sections is as follows:

\[ \text{Total Area} = \text{Width} \times (\text{Length of Section 1} + \text{Length of Section 2} + \text{Length of Section 3}) \]

Given that the width is \( 15 \), the equation becomes:

\[ 300 = 15 \times (6 + x + 4) \]

Simplifying this equation gives us:

\[ 300 = 15(10 + x) \]

Thus, the correct equation to calculate the missing length \( x \) based on the diagram described is:

\[ 15(6 + x) = 300 \]

Therefore, the correct response is:

15(6+x)=300