Question

Derek is playing a prank on Grace and hid her pencil inside a tissue box that has a width of 4 inches, a length of 8 inches, and a height of 4 inches. The pencil fits perfectly from the upper left corner to the bottom right corner of the box. What is the length of Grace’s pencil to the nearest tenth of an inch?

Answer 1

Answer: length of pencil is 9.8 inches.

Explanation:

The pencil fits perfectly from the upper left corner to the bottom right corner of the box. This is the diagonal of the box(not the diagonal of a face). To determine the length of the pencil, we would determine the length of the diagonal of the box. The formula formula is

d = √(l² + w² + h²)

Where

d = diagonal = length of pencil

w = width = 4 inches

h = height = 4 inches

l = length = 8 inches

Therefore,

d = √(4² + 4² + 8²) = √96

d = 9.8 inches

Answer 2

9.8 Inch

Explanation:

The distance from the upper left corner to the bottom right corner of the box is the longest diagonal of the box.

For a rectangular prism:

Length of the Longest diagonal
`=√( l^2+h^2+w^2)`

Therefore:

Length of the pencil
`=√( 8^2+4^2+4^2)`

`=√(96)\\=9.8$ inch(correct to the nearest tenth of an inch)`