Question

A. What is the longest poster you could fit in the box? Answer to the nearest tenth of an inch. B. Explain why you can fit only one maximum-length poster in the box, but you can fit multiple 21.5-inch posters in the same box?

Answer 1

A. Take into account that if you put the poster in the box diagonally from bottom corner to the top corner, then, the longest poster you can put into the box is given by the following diagonal:

As you can notice the value of d is the hypotenuse of a right triangle:

`d=\sqrt[]{x^2+(12)^2}`

x is also a hypotenuse of the right triangle at the base of the box:

`x=\sqrt[]{(20)^2+(8)^2}=\sqrt[]{464}`

Hence, for d you obtain:

`d=\sqrt[]{(\sqrt[]{464})^2+(144)}=\sqrt[]{646+144}=\sqrt[]{608}\approx24.66`

Hence, the maximum length of a poster you can put into the box is approximately 24.66in

B. Take into account that the diagonal of the base is:

`x=\sqrt[]{464}\approx21.5`

It means that at the base of the box you can put a poster with a length of 21.5 in. But here you are only using the base of the box. Hence, by considering the height of the box, you can notice that you can put more than one 21.5in poster into the box.