Answer:
Length= 16 inches
Width= 7 inches
Explanation:
Let's denote the width of the rectangular piece of cardboard as "w" inches.
According to the given information,
the length of the cardboard is 9 inches longer than its width, so the length can be represented as "w + 9" inches.
When the sides are folded up, the height of the box will be 2 inches.
After folding, the width of the base of the box will be "w - 4" inches, and the length will be "w + 9 - 4" inches, which simplifies to "w + 5" inches.
The volume of a rectangular box can be calculated as the product of its length, width, and height.
In this case, the volume is given as 72 in³:
Volume = Length*Width*Height
72 = (w + 5)*(w - 4) × 2
Simplifying the equation:
36 = (w + 5)*(w - 4)
Expanding the right side:
36 = w² - 4w + 5w - 20
Rearranging and combining like terms:
w² + w - 56 = 0
We can factorize by using middle term factorization:
w² + 8x-7x - 56 = 0
w(w+8)-7(w+8)=0
(w - 7)(w + 8) = 0
Setting each factor equal to zero:
either
w - 7 = 0
Therefore, w = 7
or
w + 8 = 0
w = -8 (Discard since width cannot be negative)
Therefore, the width of the piece of cardboard is 7 inches.
Substituting this value back into the expression for the length:
Length = w + 9
Length = 7 + 9
Length = 16 inches
So, the length of the piece of cardboard is 16 inches, and the width is 7 inches.