Question

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

• 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, The smaller side of rectangle be $x$ m.

$\therefore$ the diagonal of rectangle is $3x$ m.

$\therefore$ By Pythagorous theorem,

$(Diagonal{)}^2=(smallerside{)}^2+(Greaterside{)}^2$

$⟹(3x{)}^2=(x{)}^2+(Greaterside{)}^2$

$⟹(Greaterside{)}^2=9x^2-x^2=8x^2$

$⟹Greaterside=\sqrt{8x^2}=2\sqrt{2}x$

$\therefore$ Required ratio=$2\sqrt{2}x:x=2\sqrt{2}:1$