The ratio of the surface area of a rectangular prism to its volume is $$ 79: 60 $$. If the length of the prism is 5 inches and the width is 3 inches, which proportion below could be used to solve for the height? (Hint: For a rectangular prism, $$ S A=2 l w+2 w h+2 l h $$ and $$ V=l w h $$ ). $$ \frac{60}{79}=\frac{2(5)(3)+2(3)(h)+2(5)(h)}{5(3)(h)} $$ $$ \frac{79}{60}=\frac{8+h}{8 h} $$ $$ \frac{79}{60}=\frac{3+5+h}{\frac{1}{2}(3)(5)(h)} $$

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To solve for the height of the rectangular prism using the given ratio of surface area to volume, we need to first express the surface area (SA) and volume (V) in terms of the height $$ h $$.

1. **Calculate the Surface Area (SA)**:
   The formula for the surface area of a rectangular prism is:
   $$
   SA = 2lw + 2lh + 2wh
   $$
   Substituting the known values $$ l = 5 $$ inches and $$ w = 3 $$ inches:
   $$
   SA = 2(5)(3) + 2(5)(h) + 2(3)(h) = 30 + 10h + 6h = 30 + 16h
   $$

2. **Calculate the Volume (V)**:
   The formula for the volume of a rectangular prism is:
   $$
   V = lwh
   $$
   Substituting the known values:
   $$
   V = 5 \cdot 3 \cdot h = 15h
   $$

3. **Set up the ratio**:
   The ratio of the surface area to the volume is given as $$ \frac{79}{60} $$:
   $$
   \frac{SA}{V} = \frac{79}{60}
   $$
   Substituting the expressions for SA and V:
   $$
   \frac{30 + 16h}{15h} = \frac{79}{60}
   $$

Now, let's check which of the provided proportions matches this setup:

- **Option 1**: 
  $$
  \frac{60}{79} = \frac{2(5)(3) + 2(3)(h) + 2(5)(h)}{5(3)(h)}
  $$
  This simplifies to:
  $$
  \frac{60}{79} = \frac{30 + 6h + 10h}{15h} = \frac{30 + 16h}{15h}
  $$
  This is equivalent to our derived ratio.

- **Option 2**: 
  $$
  \frac{79}{60} = \frac{8+h}{8h}
  $$
  This does not match our derived ratio.

- **Option 3**: 
  $$
  \frac{79}{60} = \frac{3+5+h}{\frac{1}{2}(3)(5)(h)}
  $$
  This does not match our derived ratio.

Thus, the correct proportion that could be used to solve for the height is:
$$
\frac{60}{79} = \frac{2(5)(3) + 2(3)(h) + 2(5)(h)}{5(3)(h)}
$$
The correct proportion to solve for the height is: $$ \frac{60}{79} = \frac{2(5)(3) + 2(3)(h) + 2(5)(h)}{5(3)(h)} $$

The ratio of the surface area of a rectangular prism to its volume is . If the
length of the prism is 5 inches and the width is 3 inches, which proportion below
could be used to solve for the height?
(Hint: For a rectangular prism, and
).

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The ratio of the surface area of a rectangular prism to its volume is . If the length of the prism is 5 inches and the width is 3 inches, which proportion below could be used to solve for the height? (Hint: For a rectangular prism, and ).