Question

An auditorium is 80 m long 32 m wide and 12 m high . Find the maximum length of a rod which will measure its demonsions exactly.

Answer 1

$\underline{\pink{ Dimensions \:of \:an \: Auditorium :}}$

$Length (l) = 80 \:m ,$

$width (w) = 32 \:m$

$and \: Height (h) = 12 \:m$

$\red{ Maximum \: length \:of \: a \:rod}$

$= length \:of \:the \: diagonal$

$= \sqrt{l^{2} + w^{2} + h^{2}}$

$= \sqrt{ 80^{2} + 32^{2} + 12^{2} }$

$= \sqrt{ 6400 + 1024 + 144 }$

$= \sqrt{ 7568 }$

$\approx 86.994 \: m$

Therefore.,

$\red{ Maximum \: length \:of \: a \:rod}$

$\green { \approx 86.994 \: m}$

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Answer 2

Given :-

• Length of Auditorium (l) = 80m
• Breath of Auditorium (b) = 32m
• Height of Auditorium (h) = 12m

To Find :-

• Calculate the maximum length of a rod.

Solution :-

As we know that,

Maximum length of a rod = Length of the diagonals .

=> √ l² + b² + h²

=> √ 80² + 32² + 12²

=> √ 6400 + 1024 + 144

=> √ 7568

=> 86.994 m ( Approx)

Thus, The maximum length of a rod is 86.994m.