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Easy
Question
The dimensions of a cuboid are in the ratio of 4:3:2 and its total surface area is 1300 cm^{2 }. Find its length, breadth, and height respectively?
 10 cm , 15 cm, 20 cm
 15 cm , 10 cm ,20 cm
 15 cm , 20 cm , 10 cm
 20 cm,15cm , 10 cm
Hint:
We have given three different dimensions of rectangular box (cuboid) ,
Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
where
l → length of the cuboid
b → breadth of the cuboid
h → height of the cuboid
The correct answer is: 20 cm,15cm , 10 cm
Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1300 cm².
We have to find Length, breadth & height of cuboid.
 Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.⠀⠀
 Now, As we know that, total surface area of cuboid is given by,
Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
where, l, b & h are length, breadth and height of cuboid respectively.
 We have , length = 4x
Breadth, b = 3x
Height, h = 2x
TSA = 1300 cm^{2}
 Putting the values in the formula
 Dividing both sides of equation by 2

 Dividing both sides of equation by 26
Therefore,
The dimensions of cuboid are,
Length = 4x = 4(5)= 20
Breadth= 3x = 3(5) =15
Height = 2x=2(5)= 10
Thus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.
Therefore the correct option is d) 20 cm,15cm , 10 cm
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