SOLUTION: PLEASE HELP! and explain how you got the answer A rectangular box has a surface area of 1020 square inches, a length of 6 inches, and a width of 9 inches. Find the height. THE A

Algebra ->  Surface-area -> SOLUTION: PLEASE HELP! and explain how you got the answer A rectangular box has a surface area of 1020 square inches, a length of 6 inches, and a width of 9 inches. Find the height. THE A      Log On


   

Question 658566: PLEASE HELP!
and explain how you got the answer
A rectangular box has a surface area of 1020 square inches, a length of 6 inches, and a width of 9 inches. Find the height.
THE ANSWER IS NOT 30.4 INCHES.
Thank you!!!!!
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming the rectangular box is closed and has 6 sides, the surface area would be:
a = 2*l*w + 2*w*h + 2*h*l, so
1020+=+2%2A6%2A9+%2B+2%2A9%2Ah+%2B+2%2Ah%2A6
1020+=+108+%2B+18%2Ah+%2B+12%2Ah
18%2Ah+%2B+12%2Ah+=+1020+-+108
30%2Ah+=+912
h+=+912%2F30+=+30%2612%2F30+=+30%264%2F10+=+30.4 inches
However, this isn't the correct answer. So our initial assumption that the box is closed must be wrong. If the box is open at the top and has only a bottom and 4 sides, the surface area is
a = l*w + 2*w*h + 2*h*l, so
1020+=+6%2A9+%2B+2%2A9%2Ah+%2B+2%2Ah%2A6
1020+=+54+%2B+18%2Ah+%2B+12%2Ah
18%2Ah+%2B+12%2Ah+=+1020+-+54
30%2Ah+=+966
h+=+966%2F30+=+32%266%2F30+=+32%261%2F5+=+32.2 inches