Final answer:
To determine the longest item that can fit along the bottom of an 18x12 inch box, one must calculate the diagonal using the Pythagorean theorem. The calculation shows that the item can be approximately 21.63 inches long.
Step-by-step explanation:
The student is asking how to determine the longest item that can fit along the bottom of a box with dimensions 18 inches by 12 inches by 8 inches.
This question involves understanding the concept of the diagonal of a rectangle. To find the longest item that can fit, we need to calculate the diagonal using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length and width of the box are the sides of a right-angled triangle, and the diagonal is the hypotenuse.
Step-by-Step Calculation
Write down the dimensions of the rectangle that forms the bottom of the box: length (l) = 18 inches, width (w) = 12 inches.
Apply the Pythagorean theorem: diagonal (d) = √(l2 + w2).
Compute the diagonal: d = √(182 + 122).
Find the square values: 182 = 324, 122 = 144.
Add the square values: 324 + 144 = 468.
Take the square root: d = √468 = 21.63 inches (approx).
The longest item that can fit along the bottom of the box is approximately 21.63 inches long.