Question

The diagonal of a rectangle is thrice its smaller side. The ratio of its sides is

• A. $\sqrt{2}:1$
• B. $2\sqrt{2}:1$
• C. $3:2$
• D. $\sqrt{3}:1$

Answer 1

The correct option is B $2\sqrt{2}:1$

Let $DC=x$
and $BD=3x$



In right $\Delta BCD,$
$B{D}^2=B{C}^2+C{D}^2$
[Using Pythagoras theorem]
$\Rightarrow (3x{)}^2=B{C}^2+x^2$
$\Rightarrow 9x^2-x^2=B{C}^2$
$\Rightarrow BC=2\sqrt{2}x$
So, the longest side of the rectangle is of length $2\sqrt{2}x$ and the smallest side is x.
Thus, the ratio of the longest side to the smallest side is $2\sqrt{2}x:x=2\sqrt{2}:1$.
Hence, the correct answer is option (b).