Stuart wants to play a trick on his friend by hiding his pencil in the box of tissues shown
below. If his friend’s pencil is 9 inches in length, will it fit diagonally in the box of tissues?
Explain.
To determine if the 9-inch pencil will fit diagonally in the box of tissues, we can use the Pythagorean theorem.
The box of tissues appears to have dimensions of approximately 10 inches long, 5 inches wide, and 3 inches tall.
To find the diagonal length of the box (which is the maximum length a pencil could fit diagonally), we can imagine a right triangle with one leg being the length of the box (10 inches), another leg being the width of the box (5 inches), and the hypotenuse being the diagonal length we are trying to find.
Using the Pythagorean theorem (a^2 + b^2 = c^2), where a = 10 inches and b = 5 inches:
10^2 + 5^2 = c^2
100 + 25 = c^2
125 = c^2
c ≈ 11.18 inches
Since the diagonal length of the box of tissues is approximately 11.18 inches, the 9-inch pencil will indeed fit diagonally in the box of tissues. Stuart will successfully pull off his trick on his friend.