SOLUTION: A train ticket has an area of 192 square centimeter and a perimeter of 56 centimeters. What are the dimensions of the tickets.

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Question 744333: A train ticket has an area of 192 square centimeter and a perimeter of 56 centimeters. What are the dimensions of the tickets.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+L+ = length in cm
+W+ = width in cm
+A+ = area in cm2
+P+ = perimeter in cm
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(1) +A+=+L%2AW+
(2) +P+=+2L+%2B+2W+
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given:
(1) +192+=+L%2AW+
and
(2) +56+=+2L+%2B+2W+
(2) +L+%2B+W+=+28+
(2) +W+=+28+-+L+
By substitution:
(1) +192+=+L%2A%28+28+-+L+%29+
(1) +L%5E2+-+28L+%2B+192+=+0+
+L+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-28+
+c+=+192+
+L+=+%28-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2+-+4%2A1%2A192+%29%29+%2F+%282%2A1%29+
+L+=+%28+28+%2B-+sqrt%28+784+-+768+%29+%29+%2F+2+
+L+=+%28+28+%2B-+sqrt%28+16+%29+%29+%2F+2+
+L+=+%28+28+-+4+%29+%2F+2+
+L+=+12+
and, also
+L+=+%28+28+%2B+4+%29+%2F+2+
+L+=+16+
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If I pick the larger answer, then
(2) +W+=+28+-+L+
(2) +W+=+28+-+16+
(2) +W+=+12+
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These are the answers, because if I picked +L+=+12+,
then I would get +W+=+16+ for the width
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The length is 16 cm
The width is 12 cm