In fig, ABCD is parallelogram, $A L ⊥ C D$ and $A M ⊥ B C$ . If AB=12CM, AD=8 Cm and AL=6 cm, then AM=

15 cm

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9 cm

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10 cm

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None of these

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Solution

The correct option is B 9 cm
$A B C D$ is a parallelogram.
$A L ⊥ C D$ and $A M ⊥ B C$ [ Given ]
$A B = 12 c m,$ $A D = 8 c m$ and $A L = 6 c m$
We know, opposite sides of a parallelogram are equal.
$A B = C D$ and $A D = B C$
$∴$ $C D = 12 c m$ and $B C = 8 c m$
$\Rightarrow$ Area of a parallelogram $A B C D = A L \times C D$
$= 6 \times 12$
$= 72 c m^{2}$ ------ ( 1 )
$\Rightarrow$ Area of a parallelogram $A B C D = A M \times B C$
$= A M \times 8$ ----- ( 2 )
Comparing ( 1 ) and ( 2 ) we get,
$\Rightarrow$ $A M \times 8 = 72$
$∴$ $A M = 9 c m$

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In fig, ABCD is parallelogram, AL⊥CD and AM⊥BC. If AB=12CM, AD=8 Cm and AL=6 cm, then AM=

In fig, ABCD is parallelogram, $A L ⊥ C D$ and $A M ⊥ B C$ . If AB=12CM, AD=8 Cm and AL=6 cm, then AM=