Question

The length, breadth and height of a cuboid are in the ratio of 5:3:4, If the total surface area of the cuboid is $1504c{m}^2$, then find the dimensions of the cuboid(in $cm$).

• A. Length-20, Breadth-12, Height-16
• B. Length-28, Breadth-10, Height-15
• C. Length-24, Breadth-12, Height-20
• D. 4-Length-24, Breadth-16, Height-16

Answer 1

The correct option is A Length-20, Breadth-12, Height-16

Let the length, breadth and the height of the cuboid be $5x,3x$ and $4x$ respectively.
Total surface area = 1504
$\Rightarrow 2(lb+bh+hl)=1504$
$\Rightarrow 2(5x\times 3x+3x\times 4x+4x\times 5x)=1504$
$\Rightarrow 2(15x^2+12x^2+20x^2)=1504$
$\Rightarrow 94x^2=1504\Rightarrow x^2=\frac{1504}{94}$
$\Rightarrow x^2=16$
$\therefore x=4$
Thus, Length = $5x=5\times 4=20cm$
Breadth = $3x=3\times 4=12cm$
Height = $4x=4\times 4=16cm$
Hence, the correct answer is option (a)