What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 342 cm squared?
To find the missing length of the rectangular prism, we first need to understand that the surface area of a rectangular prism is the sum of the areas of all six faces.
Since the height and width are both 9 cm, the area of the two sides with these dimensions would be 9 cm * 9 cm = 81 cm squared for each side.
The surface area of the prism is 342 cm squared, and we already have the total area of two sides (81 cm squared each) which amounts to 162 cm squared. This leaves us with 342 cm squared - 162 cm squared = 180 cm squared for the other four sides.
Since there are four sides, and they all have the same length (which is what we are trying to find), we divide the remaining area by 4 to get the area of each of the other four sides. This gives us 180 cm squared / 4 = 45 cm squared for each side.
Since the area of a rectangle is calculated by length * width, and we have the width as 9 cm, we can find the missing length by dividing the area by the width: 45 cm squared / 9 cm = 5 cm.
Therefore, the missing length of the rectangular prism is 5 cm.