Question

In the figure, ABCD is a parallelogram with AB = 13 cm and BC = 8 cm. If O is a point on AC such that CO : OA = 2 : 3, then AE =


[1 mark]

• A. 8 cm
• B. 10 cm
• C. 12 cm
• D. 13 cm

Answer 1

The correct option is C 12 cm

Given,
$AB=13cm$

$BC=8cm$

$\text{In}\Delta \text{COB and}\Delta \text{AOE,}$

$\angle COB=\angle AOE\text{(vertically opposite angles)}$

$\angle OCB=\angle OAE\text{(alternate angles)}$

$△COB\sim △AOE\text{(by AA similarity)}$

$\therefore \frac{CO}{AO}=\frac{CB}{AE}=\frac{2}{3}$

$\Rightarrow \frac{2}{3}=\frac{8}{AE}\Rightarrow AE=12cm$