Question

In the above figure, $ABCD$ is a parallelogram, $AL\perp CD$ and $AM\perp BC$. If $AB=12cm,AD=8cm$ and $AL=6cm$, then $AM=$

• A. $15cm$
• B. $9cm$
• C. $10cm$
• D. None of these

Answer 1

The correct option is B $9cm$

$ABCD$ is a parallelogram, where $AL\perp CD$ and $AM\perp BC$

$AB=12cm,AD=8cm$ and $AL=6cm$

We know, opposite sides of a parallelogram are equal.

$AB=CD$ and $AD=BC$

$\therefore$ $CD=12cm$ and $BC=8cm$

$\Rightarrow$ Area of a parallelogram $ABCD=AL\times CD$

$=6\times 12$

$=72c{m}^2$ ------ ( 1 )

$\Rightarrow$ Area of a parallelogram $ABCD=AM\times BC$

$=AM\times 8$ ------- ( 2 )

Comparing ( 1 ) and ( 2 ), we get

$\Rightarrow$ $AM\times 8=72$

$\Rightarrow$ $AM=9cm$