Question

$ABCD$ and $BCFE$ are parallelograms. If area of $△EBC=960c{m}^2$; $AB=30cm$ and $BC=40cm$; Calculate the length of altitude from $A$ on $CD$:

• A. $32cm$
• B. $62cm$
• C. $72cm$
• D. None of these

Answer 1

The correct option is A $32cm$

$ABCD$ and $BCFE$ are parallelograms.
Area of $△EBC=960c{m}^2$
$AB=30$ cm
$BC=40$ cm
Now, let $E{E}^{\prime }$ be a altitude from $E$ to base $E{E}^{\prime }$
$\therefore$ Area of $△EBC=\frac{1}{2}BC\times E{E}^{\prime }$
$\Rightarrow E{E}^{\prime }=\frac{96}{2}$
$\Rightarrow E{E}^{\prime }=48$ cm
Area of parallelogram $ABCD=$ $BC\times$ height
$=$ $BC\times E{E}^{\prime }$
$=$ $40\times 48$
$=$ $1920c{m}^2$
Let $A{A}^{\prime }$ be the altitude to $CD$ from $A$
Now,
$AB=CD$
$\Rightarrow CD=$ $30$ cm
Now, area of parallelogram $ABCD=$ $CD\times A{A}^{\prime }$
$\Rightarrow 1920=30\times A{A}^{\prime }$
$\Rightarrow A{A}^{\prime }=\frac{1920}{30}$
$\Rightarrow A{A}^{\prime }=64$ cm