An auditorium is 80 m long 32 m wide and 12 m high . Find the maximum

1.	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» $\underline{\pink{ Dimensions \:of \:an \: Auditorium :}}$ $Length (l) = 80 \:m ,$ $width (w) = 32 \:m$ $and \: Height (h) = 12 \:m$ $\red{ Maximum \: length \:of \: a \:rod}$ $= length \:of \:the \: diagonal$ $= \sqrt{l^{2} + w^{2} + h^{2}}$ $= \sqrt{ 80^{2} + 32^{2} + 12^{2} }$ $= \sqrt{ 6400 + 1024 + 144 }$ $= \sqrt{ 7568 }$ $\approx 86.994 \: m$ THEREFORE., $\red{ Maximum \: length \:of \: a \:rod}$ $\green { \approx 86.994 \: m}$ •••♪