What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 342 cm²?
A. l = 9
B. l = 36
C. l = 5
D. None of the above
The surface area of a rectangular prism is calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the height and width are both 9 cm, we can substitute these values into the formula and the surface area equals 342 cm²:
342 = 2(9)l + 2(9)l + 2(9)(9)
342 = 18l + 18l + 162
342 = 36l + 162
180 = 36l
l = 5
Therefore, the missing length of the rectangular prism is l = 5 cm. The correct answer is C. l = 5.