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Complete Question
An open box is formed from a rectangular piece of cardboard that is 5 in. longer than it is wide, by removing squares of side 4 in. from each corner and folding up the sides. If the volume of the carton is then 336 in³, what were the dimensions of the original piece of cardboard?
Select one:
a. 15 in. by 20 in.
b. 7 in. by 12 in.
c. 11 in. by 16 in.
d. 19 in. by 24 in.
Answer:
a. 15 in. by 20 in.
Step-by-step explanation:
We are told that:
An open box is formed from a rectangular piece of cardboard that is 5 in longer than it is wide, by removing squares of side 4 in from each corner and folding up the sides.
Volume of the carton = 336 in³
Step 1
We find the area of the new piece of the cardboard
Volume of the carton/side of the square removed
= 336 in³/4 in
= 84 in²
Step 2
An open box is formed from a rectangular piece of cardboard that is 5 in longer than it is width.
Length = 5 + Width
Hence, we find the factors of 84 in² that has a difference of 5 in
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
Hence, the Factors with a difference of 5 inches = 7 and 12
The Length = 12 inches
Width is 7 inches.
The dimensions of the new piece of cardboard is 7 inches by 12 inches
Step 3
What were the dimensions of the original piece of cardboard?
Remember in the question, we are told that squares of sides 4 inches were removed from both corners
Hence,
4 inches + 4 inches = 8 inches was removed.
The dimensions of the original piece of cardboard =
Original Width = Width of the new cardboard + 8 inches
= 7 inches + 8 inches
= 15 inches.
Original length = Length of the the new cardboard + 8 inches
= 12 inches + 8 inches
= 20 inches.
Therefore, the dimensions of the original piece of cardboard is 15 inches by 20 inches
