Question

the ratio of length breadth and height of cubiod is 6:5:3 . Find the length of the cubiod of total surface area is 1332sq.cm.
Options
1) 12cm
2.15cm
3.18cm
4.20cm​

Answer 1

Let the length , Breath and height of the Cuboid be 6x, 5x, and 3x Respectively.

• Ratio of length , Breath and height = 6:5:3
• Total Surface Area = 1332 cm²

$\\ \circ \ {\pink{\underline{\boxed{\sf{ Total \ surface \ area _{(Cuboid)} = 2(lb+bh+hl) }}}}} \\ \\ \\ \colon\implies{\sf{ 1332 = 2(lb+bh+hl) }} \\ \\ \\ \colon\implies{\sf{ 1332 = 2(6x \times 5x+5x \times 3x+3x \times 6x)}} \\ \\ \\ \colon\implies{\sf{ 1332 = 2(30x^2+15x^2+18x^2 ) }} \\ \\ \\ \colon\implies{\sf{ 1332 = 2(63x^2) }} \\ \\ \\ \colon\implies{\sf{ \cancel{1332} = \cancel{126} x^2 }} \\ \\ \\ \colon\implies{\sf{10.57 \ \ \ (approx.) = x^2 }} \\ \\ \\ \colon\implies{\sf{ x = \sqrt{10.57} \mapsto 3.25 \ \ \ (approx.) }}$

Hence,

${\underline{\sf{ The \ length \ of \ the \ Cuboid \ is \ {\sf\large\bold{19.5 \ cm }} . }}}$