Question

Amir's sister is away at college and he wants to mail her a 34in baseball bat. the packaging service sells only one kind of box which measures 24in by 2in by 8 in. will the box be big enough? can someone show the work

Answer 1

How would you stuff a bat in a box that is not high enough?
Well, you'd try putting it in diagonally.
A perfect example of a pythagorean theorem problem.
Since you're looking for the diagonal value, just use the formula:
\[a^2=b^2+c^2\]
Where a is the diagonal value.
b and c are the dimensions of the box 24 and 8.
The value you get is the longest dimension you can fit in that box diagonally.
Is it bigger than 34in (size of the bat)? If yes, then you can send the bat, yay!
If it's less than 34, then you can't fit the bat, even diagonally.

Answer 2

To get the actual value for a you'd get the square root of both sides, so:
\[a=\sqrt{b^2+c^2} \]
or
\[a=\sqrt{24^2+8^2}\]

Answer 3

i still dont get it =(

Answer 4

The box is 24 by 8 so if you try to put the bat in there it will stick out by 10 inches, right?
But what if you try putting it in a diagonal.
Picture now a rectangle and you need the longest dimension you can get (to fit the bat) so you would cut the rectangle diagonally from opposite corners, this gives you a triangle with two sides forming a 90 degree angle and the hypotenuse.
That's where the formula to calculate the hypotenuse comes in.
This will give you the length of the hypotenuse, the biggest length inside the box.
So using the formula you calculate that and if it's long enough to fit the bat, you're set.
If it's not long enough to fit the bat, you can't fit the bat in.

If you still don't get it, may be tell me what part you don't get.

But I'm going to bed now, so may be I'l get to it tomorrow.