In the given figure, $A B C D$ is a parallelogram. $D L ⊥ A B$ and $A B = 13$ cm $= A D$ . If the area of parallelogram is $156 {cm}^{2}$ . Then $A L$ is _________.

5

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Solution

The correct option is A $5$ cm
Area of parallelogram ABCD $= 156 ㎠$
$A B \times D L = 156 ㎠$
$13 \times D L = 156 ㎠ \Rightarrow D L = \frac{156}{13}$ $\Rightarrow D L = 12 ㎝$
In $△ A L D,$ using Pythagoras theorem,
$A L^{2} + D L^{2} = A D^{2} \Rightarrow A L = \sqrt{13^{2} - 12^{2}} = \sqrt{25} = 5 ㎝$
$∴ A L = 5 ㎝$

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