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TEXAS INSTEL
3. Two rectangular prisms are similar and the ratio of their sides is 2:3. The surface area
of the larger rectangular prism is 2592 cm². What is the surface area of the smaller
rectangular prism?

User Waheeda
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1 Answer

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Answer:

To find the surface area of the smaller rectangular prism, we need to use the fact that the two prisms are similar and the ratio of their sides is 2:3. This means that the corresponding sides of the two prisms are in the ratio 2:3.

Let the dimensions of the smaller rectangular prism be 2x, 3x, and y, where x is a constant and y is the height. Then, the dimensions of the larger rectangular prism are 4x, 6x, and 2y.

The surface area of the smaller rectangular prism is given by:

2(2x * 3x) + 2(2x * y) + 2(3x * y) = 12x² + 4xy

We know that the surface area of the larger rectangular prism is 2592 cm², so we can set up the following equation:

2(4x * 6x) + 2(4x * 2y) + 2(6x * 2y) = 2592

Simplifying this equation gives:

72x² + 16xy = 1296

We can solve for y in terms of x by rearranging the terms:

y = (1296 - 72x²) / (16x)

Now we can substitute this expression for y into the equation

Explanation:

User Marius Gedminas
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