Question

A box is 12 in, high, 24 in. long, and 8 in. wide. What is the longest poster you could fit in
the box? Use pencil and paper. Explain why you can only fit one maximum-length poster in the box
but you can fit multiple 26-in, posters in the same box.

Answer 1

The maximum length of the poster that can be put in the box is $28in$.

Cuboid

In a cuboid, the longest dimension is the diagonal of the cuboid.

   Diagonal = $\sqrt{(length)^{2}+(width)^{2}+(height)^{2} }$

How to calculate the diagonal of a cuboid?

Let,    $l=$ the length of the cuboid

         $b=$ the width of the cuboid

         $h=$ the height of the cuboid

And   $d=$ the diagonal of the cuboid

So, as per the formulae $d=\sqrt{l^{2}+b^{2}+h^{2} }$

Assigning the given values,

$l=24$

$b=8$

$h=12$

Now, calculate $d$ using the formulae,

$d=\sqrt{24^{2}+8^{2}+12^{2}}=\sqrt{576+64+144}=\sqrt{784}=28$

Hence, the maximum length of the poster that can be put in the box is $28in$.

Learn more about the cuboid here-https://brainly.com/question/9740924

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