which equation corresponds to the following problem

Question

A=104
_____________
8[ | ]
[____|________]
n n+6
a. 8(2n+6)=104
b. 8(n+6)=104
c. 2n+6=8
d. 8+n+n+6=104

Answer 1

To analyze the problem and find the correct equation, let's break down the given information:

You have a rectangle with an area of \( A = 104 \). The rectangle has dimensions \( n \) and \( n + 6 \). The area of a rectangle is calculated as:

\[ \text{Area} = \text{length} \times \text{width} \]

In this case, the area can be represented as:

\[ A = n \times (n + 6) \]

Given that the area \( A \) is 104, we can set up the equation:

\[ n(n + 6) = 104 \]

Now, distributing \( n \) gives:

\[ n^2 + 6n = 104 \]

However, let's reframe this in terms of the options presented:

If we express it in another form, we can isolate 104:

\[ n(n + 6) = 104 \implies n^2 + 6n - 104 = 0 \]

But that doesn't directly correspond to any of the answer choices.

Now, let's check the options given:

1. a. \(8(2n+6)=104\): This indicates 8 multiplied by some quantity, but does not represent the rectangle's area effectively.

2. b. \(8(n+6)=104\): This suggests the total area is 8 times \( (n + 6) \), which doesn't match since it should not isolate the width like this.

3. c. \(2n+6=8\): This does not seem relevant because it doesn't relate to the area.

4. d. \(8+n+n+6=104\): This can be simplified to \(8 + 2n + 6 = 104\) which eventually leads back to a calculation of area, but likely doesn't represent the proper multiplication of dimensions.

Looking at the breakdown, none of the options presented captures the direct multiplication of dimensions \( n \) and \( n + 6 \) leading to an area of \( 104 \).

However, if we analyze closer, each option doesn't directly reflect the area calculation. The most logically understood formulation is indeed representing some factor of 8 as potentially coming from a width of 8 units multiplied by respective height dimensions, but from the clear structure of the area dimensions discussed, the correct area equation should simplify to reflect:

Final Conclusion

The equation distinctly representing the area based on the formulation should ideally be established as \( n(n + 6) = 104 \). Therefore, based only on the options given, none of the provided equations is exactly correct for this area representation.

If forced to choose the closest resembling form based on how 8 alters the dimension or the area assertion, we might explore d, but it's critical to understand the actual area equation itself is best expressed as \(n(n + 6) = 104\).