Question

Maths the dimensons of a cuboid are in the ratio 3:4:5 and its total surface area is 3384 cm2. Find the diamensions of the cuboid

Answer 1

$\bold{Given}$

$\mathsf{Surface \: area \: of \: cubiod= 3384 \: cm^{2}}$

$\textsf{The \: dimensions \: of \: an \: cubiod \: are \: in \: ratio \: 3 : 4 : 5}$

$\textsf{Let \: the \: common \: ratio \: be \: x}$

$\textsf{So, \: sides \: becomes}$

$\mathsf{Length \: l= 3x}$

$\mathsf{Breadth \: b = 4x}$

$\mathsf{Height \: h= 5x}$

$\textsf{We \: know, }$

$\large \boxed{\mathsf{Surface \: area = 2(lb + bh + hl)}}$

$\textsf{On \: placing \: values}$

$\mathsf{Surface \: area = 2(3x \times 4x + 4x \times 5x + 5x \times 3x )}$

$\mathsf{Surface \: area = 2( 12x + 20x + 15x)}$

$\mathsf{Surface \: area = 2(47x)}$

$\mathsf{Surface \: area = 94x}$

$\textsf{Since, }$

$\mathsf{Surface \: area \: of \: cubiod= 3384 \: cm^{2}}$

$\textsf{So, }$

$\mathsf{3384 = 94x}$

$\mathsf{\dfrac{3384}{94} = x}$

$\large \boxed{\mathsf{x = 36}}$

$\textsf{Dimensions \: of \: cubiod \f will \: be, }$

$\mathsf{Length \: l= 3 \times 36 = 108 cm}$

$\mathsf{Breadth \: b = 4 \times 36 = 144 cm}$

$\mathsf{Height \: h= 5 \times 36 = 180 cm}$