Question 205122
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Your answer is:
length of the package is 24 inches
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Here's how it was found.
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length of your package is represented by the lines:
AB, DC, HG, and EF
also R2AR2B and R2DR2C
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width of your package is represented by the lines:
AD, BC, FG, EH
also R1AR1B and R1DR1C
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the height of your package is represented by the lines:
AE, BF, CG, DH
also R1AR1D, R1BR1C, R2BR2C, R2AR2D
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Your first ribbon is R1 and it goes around 2 times the height and 2 times the width.
Your second ribbon is R2 and it goes around 2 times the height and 2 times the length.
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your height = H
your width = W = H+6
your length = L = W+12
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R1 + R2 = 96 inches.
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R1 = 2H + 2W
R2 = 2H + 2L
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Since W = H+6, then:
R1 = 2H + 2(H+6) = 2H + 2H + 12 = 4H + 12
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Since L = W + 12 and W = H + 6 then:
L = (H+6) + 12 = H + 18 and:
R2 = 2H + 2L = 2H + 2*(H+18) = 2H + 2H + 36 = 4H + 36
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We have:
R1 = 4H + 12
R2 = 4H + 36
R1 + R2 = 96
4H + 12 + 4H + 36 = 96
combine like terms to get:
8H + 48 = 96
subtract 48 from both sides to get:
8H = 48
divide both sides by 8 to get:
H = 6
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We have H = 6
W = H + 6 so W = 12
L = W + 12 so L = 24
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H = 6
W = 12
L = 24
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going back to the ribbons.
R1 = 2H + 2W = 2*6 + 2*12 = 12 + 24 = 36 inches.
R2 = 2H + 2L = 2*6 + 2*24 = 12 + 48 = 60 inches.
R1 + R2 = 36 + 60 = 96 inches.
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Everything checks out so the length of your package = L = 24 inches.
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