Question

the dimensions of a cuboid are in the ratio 3:4:5 & its total surface area is 3384cm2.Find the dimensions of the solid.

Answer 1

Answer:

$Let\:the\:dimensions\:of\:\\cuboid\:be\:=\:3x\::\:4x\::\:5x\\T.S.A.\:of\:cuboid\:=\:3384cm^{2}\\A/q\\\:=>\:2(lb\:+\:bh\:+\:lh)\:=\:3384cm^{2}\\\:=>\:2(3x*4x\:+\:4x*5x\:+\:3x*5x)\:=\:3384\\\:=>\:2(12x^{2}\:+\:20x^{2}\:+\:15x^{2})\:=\:3384\\\:=>\:2*47x^{2}\:=\:3384\\\:=>\:94x^{2}\:=\:3384\\\:=>\:x^{2}\:=\:\frac{3384}{94}\:=\:36\\\:=>\:x\:=\:\sqrt{36} \\\:=>\:x\:=\:\sqrt{6*6}\\\:=>\:x\:=\:6\\\\Hence,\:the\:dimensions\:of\:cuboid\:are:\\3x=3*6=18cm\\4x=4*6=24cm\\5x=5*6=30cm$