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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?

The ratio of the surface area of a rectangular prism to its volume is 79:60. If the-example-1

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Answer: 60(30) + 16h) = 79(15h)

Let's call the height of the rectangular prism "h".

The surface area of a rectangular prism is given by the formula:

SA = 2lw + 2lh + 2wh

The volume of a rectangular prism is given by the formula:

V = lwh

We're given that the ratio of the surface area to the volume is 79:60. So, we can write:

SA/V = 79/60

Substituting the values for the length, width, and height of the prism, we get:

(2(5)(3) + 2(5)(h) + 2(3)(h)) / (5)(3)(h) = 79/60

Simplifying the left-hand side, we get:

(30 + 10h + 6h) / 15h = 79/60

Combining like terms on the numerator, we get:

(30 + 16h) / 15h = 79/60

Cross-multiplying, we get:

60(30 + 16h) = 79(15h)

Expanding and simplifying, we get:

1800 + 960h = 1185h

Subtracting 960h from both sides, we get:

1800 = 225h

Dividing both sides by 225, we get:

h = 8

So, the height of the rectangular prism is 8 inches.

To solve for the height using a proportion, we can set up the following proportion:

(2lw + 2lh + 2wh) / lwh = 79/60

Substituting the given values, we get:

(2(5)(3) + 2(5)(h) + 2(3)(h)) / (5)(3)(h) = 79/60

Simplifying the left-hand side, we get:

(30 + 10h + 6h) / 15h = 79/60

Cross-multiplying, we get:

60(30 + 16h) = 79(15h)

We can then solve for h using algebraic manipulation as shown earlier.

User Reachlin
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