The original dimensions (length and width) of this rectangular piece of metal are 19.81 inches and 14.81 inches respectively.
Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume = L × W × H
Where:
Given the following data:
Length, L = W + 5
Since squares of 1 in long are cut from the four corners, the length and width are reduced by 2 in. Also, the height of the box would be 1 inches.
Therefore, the volume of this rectangular box is given by:
456 = (L - 2) × (W - 2) × 2
456 = (W + 5 - 2) × (W - 2) × 2
456 = (W + 3) × (W - 2) × 2
228 = (W² - 2W + 3W - 6)
228 = W² + W - 6
W² + W - 6 - 228 = 0
W² + W - 234 = 0
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]W = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\W = \frac{-1\; \pm \;\sqrt{1^2 - 4(1)(-234)}}{2 \times 1}\\\\W = \frac{-1\; \pm \;\sqrt{1 + 936}}{2}\\\\W = \frac{-1\; \pm \;\sqrt{937}}{2}[/tex]
Width, W = 14.81 or -15.81
Since the width cannot be negative, the value of W is equal to 14.81 inches.
For the length, we have:
Length, L = W + 5
Length, L = 14.81 + 5
Length, L = 19.81 inches.
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