Question

At a restaurant, a trash can’s opening is rectangular and measures 7 inches by 9 inches. The restaurant serves food on trays that measure 12 inches by 16 inches. Jada says it is impossible for the tray to accidentally fall through the trash can opening because the shortest side of the tray is longer than either edge of the opening. Do you agree or disagree with Jada’s explanation? Explain your reasoning.

Answer 1

Answer:

I agree it won't fit, but not because of Jada's explanation

Step-by-step explanation:

The trash can's opening measures 7 inches by 9 inches and the trays measure 12 inches by 16 inches. It's obvious that the trays won't fit through the opening if they are tried by the opening's width or height, but what if we try to make the tray go through the diagonal of the opening?

We must then compute the length of the opening's diagonal, if it's longer than any of the tray's dimensions, then it can fall through it.

$d=\sqrt{7^2+9^2}=11.4\ in$

The diagonal is shorter than the shortest side of the tray, so it's impossible to fall through the opening, but not for the reason explained by Jada. Some calculation should be done before stating it.