SOLUTION: Okay, my question is as follows: A team is to design a cover a box to hold a jigsaw puzzle. The design will use 525 square cm. The cardboard is precut to 29 cm x 33 cm. The d

Algebra ->  Equations -> SOLUTION: Okay, my question is as follows: A team is to design a cover a box to hold a jigsaw puzzle. The design will use 525 square cm. The cardboard is precut to 29 cm x 33 cm. The d      Log On


   



Question 237439: Okay, my question is as follows:
A team is to design a cover a box to hold a jigsaw puzzle. The design will use 525 square cm. The cardboard is precut to 29 cm x 33 cm. The depth of the box (x) can vary to fit the needs of your cover design. How deep should the box be in order to allow the area of 525 cm for your design? I'm puzzled at how to set up this problem...please help me! Thanks!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
With these box problems, what they do,
usually, is cut small squares out of the corners
and then fold up the 4 equal height sides to
make the box.
So, I'll say that each of these 4 equal squares will have
dimensions x%2Ax+=+x%5E2 cm2
To get the area of the bottom after the sides are
folded up, I subtract 2x from each side.
%2829+-+2x%29%2A%2833+-+2x%29+=+525
957+-66x+-58x+%2B+4x%5E2+=+525
957+-+124x+%2B+4x%5E2+=+525
4x%5E2+-+124x+%2B+432+=+0
x%5E2+-+31x+%2B+108+=+0
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+-31
c+=+108
x+=+%28-%28-31%29+%2B-+sqrt%28+%28-31%29%5E2-4%2A1%2A108+%29%29%2F%282%2A1%29+
x+=+%28+31+%2B-+sqrt%28+961+-+432+%29%29%2F2+
x+=+%28+31+%2B-+sqrt%28+529+%29%29%2F2+
x+=+%28+31+%2B-+23%29%2F2+
x+=+%2831+-+23%29%2F2
x+=+8%2F2
x+=+4
and
x+=+31+%2B+23%29%2F2
x+=+54%2F2
x+=+27 (can't be answer, too big)
The box has to be 4 cm deep
check answer:
%2829+-+2x%29%2A%2833+-+2x%29+=+525
%2829+-+2%2A4%29%2A%2833+-+2%2A4%29+=+525
%2829+-+8%29%2A%2833+-+8%29+=+525
21%2A25+=+525
525+=+525
OK