Final answer:
To find the dimensions of the second rectangular prism, you need to calculate the surface area of the first prism. The surface area is found using the formula SA = 2lw + 2lh + 2wh. Setting the surface area of the second prism equal to the first, you can solve for the dimensions. The dimensions of the second prism are length = (128 - 8y) / (2y + 10), width = y, and height = 6 m.
Step-by-step explanation:
In order to find the dimensions of a second rectangular prism that will have the same surface area as the first one, you need to calculate the surface area of the first prism. The surface area of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.
For the first prism, l = 5 m, w = 4 m, and h = 6 m. Plugging these values into the formula, we get: SA = 2(5)(4) + 2(5)(6) + 2(4)(6) = 20 + 60 + 48 = 128 square meters.
Now, let's find the dimensions of the second prism. Since the surface area of both prisms is the same, we can set up the equation: 2lw + 2lh + 2wh = 128. We know that the length and width of the second prism will be the same as the first prism, so we can substitute those values. Let's say the length and width of the second prism are x and y, respectively. Substituting those into the equation, we get: 2xy + 2(5)(x) + 2(4)(y) = 128.
Simplifying the equation, we get: 2xy + 10x + 8y = 128. This equation can be rearranged to: x(2y + 10) + 8y = 128. We can solve for x in terms of y by subtracting 8y from both sides: x(2y + 10) = 128 - 8y. Dividing both sides by 2y + 10, we get: x = (128 - 8y) / (2y + 10).
So, the dimensions of the second rectangular prism that will have the same surface area as the first one are: length = (128 - 8y) / (2y + 10), width = y, and height = 6 m.