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# The total surface area of a cube is 846 cm^{2}. 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:

### 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 = 846cm^{2}

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(47x^{2}) = 846

Divide both sides by 2,

Divide both sides by 47,

Taking square root

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.

^{2}) = 846

Divide both sides by 2,

Divide both sides by 47,

Taking square root

The dimensions of cuboid are,

Therefore the option a)15cm , 12cm , 9cm is correct.

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