Question

ABCD is a quadrilateral such that $AB=BC$, $AD=\frac{1}{2}CD$ and $AD=\frac{1}{4}AB$. If $BC=12$ cm, what is the measures of AD?

• A. $6$ cm
• B. $4$ cm
• C. $12$ cm
• D. $3$ cm

Answer 1

The correct option is D $3$ cm

$\Rightarrow$ In quadrlateral ABCD,

$\Rightarrow$ AB = BC [Given] --- ( 1 )

$\Rightarrow$ BC = 12cm. [Given]

$\Rightarrow$ AB = 12cm. [From ( 1 )]

$\Rightarrow$ It is given that, $AD=\frac{1}{4}AB$

$\Rightarrow$ $AD=\frac{1}{4}\times 12$ [Substituting value of AB]

$\therefore$ $AD=3cm.$