Question

ABCD is a rectangle of dimensions 6 cm $\times$ 8 cm. DE and BF are the perpendiculars drawn on the diagonal of the rectangle. What is the ratio of the shaded to that of unshaded region?

• A. 7 : 3
• B. 16 : 9
• C. $4:3\sqrt{2}$
• D. Data insufficient

Answer 1

The correct option is B 16 : 9

$\frac{Areaof\Delta DAE}{Areaof\Delta DEC}=\frac{\frac{1}{2}\times DE\times AE}{\frac{1}{2}\times DE\times CE}=\frac{AE}{CE}=\frac{(AD{)}^2}{(DC{)}^2}={\left(\frac{6}{8}\right)}^2=\frac{9}{16}Similarly,in\Delta ABC,\frac{Areaof\Delta BCF}{Areaof\Delta BFA}=\frac{9}{16}$
$\therefore$ The area of shaded to unshaded region $=\frac{16}{9}$