geometry work problem

Question

Amaris sister is away at college and he wants to mail her a 34 in. Baseball bat. The packaging service sells only one kind of box, which measures 24 in. By 20 in. By 12 in. What is the length of the diagonal of the box? Will the box be big enough?

Answer 1

The sum of the  squares of each leg of a right angle is equal to the square of the hypotenuse. Assume the bottom of the box is 20 x 24 in.

 

20^2 + 24^2 = 400 + 576 = 976

The square root of 976 = 31.24

 

Now the 31.24 inch hypotenuse forms a right angle to the height of the box.

 

12^2 + 31.24^2 = 144 + 976 = 1,120 which is the hypotenuse from a lower right corner to the upper left corner, the longest length in the box.

 

And the square root of 1,120 = 33.46 inches, which is not quite enough to hold the bat.