Question

 If the ratio of the greater angle between diagonals of a rectangle to the 

smaller angle is 2: 1 and a > b then, the ratio a: b of sides of the rectangle is?

Answer 1

Given $\varphi=2 (180^0-\varphi)$

$\varphi=360^0-2\varphi$

$3\varphi=360^0$

$\varphi=120^0$

$cot 30^0 = \frac{a}{b} \implies a:b = \sqrt{3}: 1$