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The wall of downtown recreation center are being covered with paneling.the doorway into one room is 1 meter wide and 3 meters hight.whats the longest length of the longest rectangular panel that can be taken though the doorway

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bartdrinksmalk
The longest length through a rectangle is the diagonal.

We use the Pythagorean Theorem:
[tex]c^{2}=a^{2}+b^{2}[/tex]
⇒[tex]c^{2}=1^{2}+3^{2}[/tex]
⇒[tex]c^{2}=1+9[/tex]
⇒[tex]c^{2}=10[/tex]
⇒[tex]c=\sqrt{10}[/tex]

So the longest length that can be taken through the doorway is [tex]\sqrt{10}[/tex].

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