Question

A room is in the form of cuboid it measures 7.2m×9.6×3.5m find
a) length of diagonal on any one face
b) longest stick that could be accommodated in room

Answer 1

$\underline { \blue { Dimensions \:of \: a \:room : }}$

$Length (l) = 7.2 \:m \: Breadth (b) = 9.6 \:m \\and \: height (h) = 3.5\:cm$

$\red{ a) Length \:of \: diagonal \:on \:one }\\\red{face} = \sqrt{l^{2} + b^{2} }\\= \sqrt{ 7.2^{2} + 9.6^{2}} \\= \sqrt{ 51.84 + 92.16} \\= \sqrt{144}\\= \sqrt{12^{2}} \\= 12 \:m$

$\red{ Longest \:stick \: that \: could \: be }\\\red{accommodated\:in \:room } \\= \sqrt{l^{2} + b^{2} + h^{2}} \\= \sqrt{ 7.2^{2} + 9.6^{2} + 3.5^{2} } \\= \sqrt{ 51.84 + 92.16 + 12.25 } \\= \sqrt{156.25} \\= 12.5 \:m$

Therefore.,

$\red{ a) Length \:of \: diagonal \:on \:one }\\\red{face} \green { = 12 \:m }$

$\red{ Longest \:stick \: that \: could \: be }\\\red{accommodated\:in \:room } \green {= 12.5\:m }$

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