To find the equation for the missing length based on the information given, we start by identifying the components of the rectangular plot's area. The area of a rectangle is calculated by multiplying its length (L) by its width (W):
\[ \text{Area} = L \times W \]
In your case, the area is given as 300 square feet, and you mentioned the plot has dimensions involving some variables.
If we assume one dimension of the rectangle is 15 feet (which is a common value for width or length in other examples) and the other dimension involves a variable (x or another expression), we can set up the equation accordingly.
Given the options you've provided, we can reason through:
- 15(x+10) = 300 - This suggests one dimension is 15 feet, and the other is expressed as (x + 10).
- 15(6+x) = 300 - This indicates one dimension is also 15 feet, and the other as (6 + x).
- 15x = 300 - This indicates that the width or length is directly expressed in terms of x.
- 15(6) + x + 15(4) = 300 - This does not follow the standard rectangle area formula because it adds multiple dimensions which does not represent the area correctly.
To find the missing length based on your choices, let's verify which one correctly computes to give the area of 300 square feet.
Assuming one dimension is 15, then:
For 15(x + 10) = 300:
- Divide both sides by 15: \(x + 10 = 20\) → \(x = 10\)
For 15(6 + x) = 300:
- Divide both sides by 15: \(6 + x = 20\) → \(x = 14\)
For 15x = 300:
- Divide both sides by 15: \(x = 20\)
Given that none of these contradictory dimensions seem right without additional information, 15x = 300 assumes a straightforward case of dimension x being directly proportional.
Based on the standard setup for area assuming one of the dimensions as a constant (15), the correct calculation choice among those provided would be:
15x = 300.
This directly suggests that x is the missing length computed based off an area-defined relationship.
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