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Maths-

General

Easy

Question

The total surface area of a cube is 846 cm². Find the height, breadth, and length if the dimensions are in the ratio of 3:4:5

15 cm, 12 cm and 9 cm
12 cm , 9 cm and 18 cm
15 cm , 24 cm ,9 cm
9 cm , 24 cm ,15 cm

hint Hint:

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
Where,
l = length
b = breadth
h = height

The correct answer is: 15 cm, 12 cm and 9 cm

We have given the surface area of cube = 846cm²
And the ratio of height breadth and length is 3:4:5
Let , height = 3x,
Breadth =4x,
Length = 5x
Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
$2 left square bracket left parenthesis 5 x right parenthesis left parenthesis 4 x right parenthesis plus left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 5 x right parenthesis left parenthesis 3 x right parenthesis right square bracket equals 846$

$2 open square brackets 20 x squared plus 12 x squared plus 15 x squared close square brackets equals 846$
2(47x²) = 846
Divide both sides by 2,
$table attributes columnspacing 1em end attributes row cell 47 x squared equals 846 over 2 end cell row cell 47 x squared equals 423 end cell end table$
Divide both sides by 47,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 423 over 47 end cell row cell x squared equals 9 end cell end table$
Taking square root
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals square root of 9 end cell row cell x equals 3 end cell end table$
The dimensions of cuboid are,
Height = 3x=3(3)= 9
Breadth= 4x =4(3) =12
Length = 5x = 5(3)= 15
Therefore the option a)15cm , 12cm , 9cm is correct.

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