Let the missing length be x cm.
The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
We are given that the height and width are both 9 cm, so we can substitute those values in and simplify:
432 = 2lx + 2(9)(x) + 2(9)(l)
432 = 2x(l + 9 + 9)
432 = 2x(l + 18)
216 = x(l + 18)
We don't have enough information to solve for both x and l, but we can use some guess and check. We know that the length, l, must be a multiple of 6 (since 216 is divisible by 6), and it must be greater than 9 (since the missing length cannot be shorter than either the height or width). Let's try some values for l:
If l = 12, then x = 12, and the surface area would be:
SA = 2(12)(9) + 2(12)(9) + 2(9)(9)
SA = 432
So, the missing length is 12 cm.
What is the missing length of a rectangular prism where the height and width are both 9 cm in the surface area is 432 cm²
1 answer