Question

the diagonal of a cuboid is 12 centimetre and the sum of its Length breadth and height is 17 cm find the total surface area​

Answer 1

Step-by-step explanation:

Let the length, breadth and height of the cuboid be l, b and h respectively.

$Length \: of \: diagonal = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } \\ \therefore \: 12 = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } \\ squiring \: both \: sides \: we \: find: \\ {12}^{2} = (\sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } )^{2} \\ \implies \: {l}^{2} + {b}^{2} + {h}^{2} = 144...(1) \\ Now, \\ l + b + h = 17... (Given) \\ squiring \: both \: sides \: we \: find: \\ ( l + b + h)^{2} = (17)^{2} \\ {l}^{2} + {b}^{2} + {h}^{2} + 2lb + \:2 bh + \:2 hl = 289 \\ .....(2) \\ from \: equations \: (1) \: and \: (2) \: we \: find : \\ 144 + 2lb + \:2 bh + \:2 hl = 289 \\ 2lb + \:2 bh + \:2 hl = 289 - 144 \\ 2(lb + \: bh + \: hl ) = 145 \\ \because \: total \: surface \: area \: of \: cuboid \: \\ = 2(lb + \: bh + \: hl ) \\ \therefore \: total \: surface \: area \: of \: cuboid \: \\ = 145 \: {cm}^{2}$