Question

The length, breadth and height of a rectangular solid are in the ratio $5:4:2$. If the total surface area is $1216$ cm${}^2$, find the length, breath and height of the solid.

• A. $20$ cm, $16$ cm, $8$ cm
• B. $14$ cm, $12$ cm, $8$ cm
• C. $11$ cm, $19$ cm, $8$ cm
• D. $21$ cm, $11$ cm, $8$ cm

Answer 1

The correct option is A $20$ cm, $16$ cm, $8$ cm

Given length, breadth and height of a cuboid are in ratio $5:4:2$. Also given total surface area of cuboid is $1216$ cm${}^2$.
Let length, breadth and height of a cuboid be $5x,4x$ and $2x$ respectively.
So, total surface area of cuboid $=2(lb+bh+lb)=2(5x\times 4x+4x\times 2x+5x\times 2x)=2(20x^2+8x^2+10x^2)=2\left(38x^2\right)=76x^2$
Total surface area of cuboid $=1216$ cm ${}^2$
$\Rightarrow 76x^2=1216{cm}^2$

$\Rightarrow x^2=16\therefore x=4,x=-4$

$x=-4$ is neglected because length cannot be negative.
$\therefore$ dimensions of cuboid are :
Length $=5x=5\times 4=20$ cm
Breadth $=4x=4\times 4=16$ cm
Height $=2x=2\times 4=8$ cm