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In figure, ABCD is a parallelogram, $D L ⊥ A B$ . If $A B = 20 cm, A D = 13 cm$ and area of the parallelogram is $100 cm 2$ , find AL

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10 cm

12 cm

15 cm

17 cm

answer is B.

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Detailed Solution

Given ABCD is a parallelogram,

D L ⊥ A B

and AB = 20 cm and AD = 13 cm and area of the parallelogram is

100 cm 2

In the given figure, ABCD is a parallelogram. DL is perpendicular to AB and AB = AD =13 cm. If the area of the parallelogram is 156 cm 2, then find the

Assume, the height = x.
The area of parallelogram is,

A r e a = b a s e × h e i g h t ⇒ 20 × x = 100

⇒ x = 10020

⇒ x = 5

Assume, AL = y.
Apply Pythagoras theorem in ∆ADL,

h y p o t e n u s 2 = p e r p e n d i c u l a r 2 + b a s e 2 b a s e 2 = h y p o t e n u s 2 − p e r p e n d i c u l a r 2 b a s e = h y p o t e n u s 2 − p e r p e n d i c u l a r 2

⇒ y = 132 − 52

⇒ y = 169 − 25

⇒ y = 144

⇒ y = 12

Therefore, the length AL is 12 cm.
Hence, option 2 is correct.

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