Question

Martin wants to ship a souvenir baseball bat that is 16 inches long in this box.

Will Martin be able to ship the bat in that box?

Answer 1

Explanation:

Remark

The first job is to find the diagonal along the bottom. Pretend that the sides and top do not exist for just a moment.

Givens

It becomes a Pythagorean problem.

a = 12

b = 9

c = ?

Solution

a^2 + b^2 = c^2

144 + 81 = c^2

c^2 = 225

sqrt(c^2) = sqrt(225)

c = 15

Remark

Now you look at the diagram again, a little more closely this time.

The diagonal that you want is from the lower right to the upper closest left.

c = 15

d = 8

e = ?

e^2 = c^2 + d^2

e^2 = 15^2 + 8^2

e^2 = 225 + 64

e^2 = 289

e = 17

The shipping box is large enough

Note

There is one think you can note

You can do this entire problem in one step

a = 12 b = 9 c= 8

a^2 + b^2 + c^2 = diagonal from lower right to upper left^2

12^2 + 9^2 + 8^2 = diagonal^2

144 + 81 + 64 = diagonal ^2

289 = diagonal^2

diagonal = 17 just as it did before.