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: