Question

The surface area of a cuboid is 1372 $c{m}^2$. If the ratio length : breadth : height is 4:2:1, then its length (in $cm$) is

• A. 7
• B. 14
• C. 21
• D. 28

Answer 1

The correct option is D

28

S.A. = 1372 $c{m}^2$ (Given)

$\Rightarrow 2(l\times b+b\times h+l\times h)=1372$

$[\because$ Surface area of a cuboid of dimensions $l\times b\times h$ is given by $2(lb+bh+lh).]$

Also, it is given that $l:b:h=4:2:1$.

Let $l=4k,b=2k$ and $h=k$.

$\text{Then,}2(4k\times 2k+2k\times k+4k\times k)=1372$

$⟹28k^2=1372$

$⟹k^2=49$

$⟹k=7$

$\therefore l=4k=4\times 7=28\text{cm}$