Question

The internal dimensions of a rectangular box are $12$ cm $\times x$ cm $\times 9$. If the length of the longest rod that can be placed in this box is $17$ cm; find $x$.

• A. $8$ cm
• B. $6$ cm
• C. $4$ cm
• D. $2$ cm

Answer 1

The correct option is A $8$ cm

Dimensions of rectangular box are:

$l=12$

$b=x$

$h=9$

The length of longest rod that can be placed in the box will be along central diagonal.

Length of central diagonal is

$k=\sqrt{l^2+b^2+h^2}$

$\Rightarrow 17=\sqrt{{12}^2+x^2+9^2}$

$\Rightarrow 17=\sqrt{144+x^2+81}$

$\Rightarrow 289=225+x^2$

$\Rightarrow x=\sqrt{64}=8$

So $x=8$