Question

The areas of the adjacent faces of a rectangular block are in the ratio $2:3:4$ and its volume is $9000c{m}^3$. Find the length of its shortest edge

• A. $30cm$
• B. $20cm$
• C. $15cm$
• D. $10cm$

Answer 1

The correct option is C $15cm$

area of $ABCD=lh$

area of $CFBG=bh$

area of $DCEF=l\times b$

$bh:lb:lh=2:3:4$

$\Rightarrow \frac{h}{l}=\frac{2}{3}$ $\frac{b}{h}=\frac{3}{4}$ $\frac{b}{l}=\frac{1}{2}$

$lbh=9000c{m}^3$

$\Rightarrow \left(2b\right)b\times \left(\frac{4}{3}b\right)=9000$

$\Rightarrow b^3=\frac{27000}{8}$

$\Rightarrow b=15cm,l=30cm,h=20cm$

$\therefore$ Shortest edge is $15cm$