Question

In quadrilateral ABCD, its diagonals AC and BD intersect at point O such that $\frac{OC}{OA}=\frac{OD}{OB}=\frac{1}{3}$

If CD =4.5 cm; find the length of AB.

• A. 12 cm
• B. 14.5 cm
• C. 13.5 cm
• D. 11.8 cm

Answer 1

The correct option is C

13.5 cm

In quadrilateral ABCD, diagonals AC and BD intersect each other at O and $\frac{OC}{OA}=\frac{OD}{OB}=\frac{1}{3}$

In $\Delta OAB$ and $\Delta OCD$

$\angle COD=\angle AOB$ (Vertically opp. angles)

$\frac{OC}{OA}=\frac{OD}{OB}=\frac{1}{3}$ (given)

$\therefore \Delta OAB\sim \Delta OCD$ (SAS axiom)

$\frac{OA}{OC}=\frac{OB}{OD}=\frac{AB}{CD}$

$\because \frac{CD}{AB}=\frac{1}{3}\Rightarrow \frac{4.5}{AB}=\frac{1}{3}$

$AB=4.5\times 3=13.5cm$