a rectangular prism has a total surface area of 166mm^2, a height of 4mm, a width of 5mm. what is the length of the prism?
If the length is x, then
2*4*5 + 2*5x + 2*4x = 166
Now just solve for x
To find the length of the rectangular prism, we need to use the given information about its total surface area, height, and width.
The total surface area of the rectangular prism is the sum of the areas of all six faces. Since we have the width, height, and total surface area given, we can set up an equation to solve for the length.
To find the area of a rectangle, we multiply its length by its width. Since two opposite faces of the rectangular prism have the same dimensions, the width and height can be used to calculate the surface area of those two faces.
Let's break down the surface area calculation:
1. We have two faces with the dimensions length × height: 2 × (length × height).
2. We have two faces with the dimensions length × width: 2 × (length × width).
3. We have two faces with the dimensions width × height: 2 × (width × height).
Adding up these three areas gives us the total surface area:
2(length × height) + 2(length × width) + 2(width × height) = 166 mm²
Substituting the given values:
2(4 mm × length) + 2(5 mm × length) + 2(5 mm × 4 mm) = 166 mm²
Now, we can solve this equation to find the length.