what is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432cm squared?
To find the missing length of the rectangular prism, we can 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 equation:
432 = 2l(9) + 2(9)h + 2(9)h
432 = 18l + 36h
Since the height and width are equal, we can simplify the equation further:
432 = 18l + 72
Now, we can isolate the length (l) by subtracting 72 from both sides and then dividing by 18:
360 = 18l
l = 20
Therefore, the missing length of the rectangular prism is 20 cm.