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 in what were the dimensions of the original piece of cardboard?

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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.

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

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