Answer:
[tex]2\sqrt{42}[/tex]
Step-by-step explanation:
Given
[tex]l = 10in[/tex] --- Length
[tex]w = 8in[/tex] --- Width
[tex]h = 2in[/tex] --- Height
Required: Determine the length of the straw
Since the straw fits the diagonal of the box, the length of the straw is equivalent of the length of the diagonal.
The length of the diagonal is calculated as:
[tex]\displaystyle d = \sqrt{w^{2} + l^{2} + h^{2}}[/tex]
[tex]\displaystyle d = \sqrt{8^{2} + 10^{2} + 2^{2}}[/tex]
[tex]\displaystyle d = \sqrt{64 + 100 + 4}[/tex]
[tex]\displaystyle d = \sqrt{168}[/tex]
[tex]\displaystyle d = \sqrt{4*42}[/tex]
Split
[tex]\displaystyle d = \sqrt{4}*\sqrt{42}[/tex]
[tex]\displaystyle d = 2*\sqrt{42}[/tex]
[tex]\displaystyle d = 2\sqrt{42}[/tex]
Hence, the straw length is: [tex]2\sqrt{42}[/tex]
