Question

The diagonal of a rectangle is thrice its smaller side The ratio of the side is

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

Answer 1

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

Let the sides of rectangle is a and b resp.

Then one diagonal =3b

then $(3b{)}^2=a^2=b^2$

$\Rightarrow b^2=9a^2-a^2$

$\Rightarrow b^2=8a^2$

$\Rightarrow b=2\sqrt{2}a$

Then one side =b and second side =$2\sqrt{2}b$

So ratio =$\frac{2\sqrt{2}b}{b}=\frac{2\sqrt{2}}{1}$