SOLUTION: Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard into a closed rectangular box. The four sides of the box have the same area, an

Algebra ->  Surface-area -> SOLUTION: Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard into a closed rectangular box. The four sides of the box have the same area, an      Log On


   

Question 1059101: Bill has a sheet of cardboard with an area of 10 square feet. He makes the entire sheet of cardboard into a closed rectangular box. The four sides of the box have the same area, and the two ends have the same area. The area of each of the four equal sides is twice the area of each end. What is the area of each face of Bill's box?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the area in ft2 of one of the sides
Let +b+ = the area of top or the bottom in ft2
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(1) +4a+%2B+2b+=+10+
(2) +a+=+2b+
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Plug (2) into (1)
(1) +4%2A%282b%29+%2B+2b+=+10+
(1) +8b+%2B+2b+=+10+
(1) +10b+=+10+
(1) +b+=+1+
and
(2) +a+=+2b+
(2) +a+=+2%2A1+
(2) +a+=+2+
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The area of each of the side faces is 2 ft2
The area of top is 1 ft2
The area of the bottom is 1 ft2