what is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm ^2?
To find the missing length of the rectangular prism, we need to use the formula for the surface area of a rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Given that the height and width are both 9 cm, we can substitute these values into the formula:
432 = 2(x)(9) + 2(9)(9) + 2(9)(x)
Now, simplify the equation:
432 = 18x + 162 + 18x
432 = 36x + 162
270 = 36x
x = 7.5 cm
Therefore, the missing length of the rectangular prism is 7.5 cm.