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In figure, if AB = 35 cm and AD = 20 cm and area of the parallelogram is $560 cm 2,$ find LB.

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23 cm

25 cm

28 cm

32 cm

answer is A.

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Detailed Solution

Given a figure in which AB = 35 cm and AD = 20 cm and area of the parallelogram is

560 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, DL = x.
The area is,

A r e a = b a s e × h e i g h t ⇒ 35 × x = 560

⇒ x = 56035

⇒ x = 16

Assume, AL = y.
Applying Pythagoras theorem in ∆ DAL,

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

⇒ y = 202 − 162

⇒ y = 400 − 256

⇒ y = 144

⇒ y = 12

Therefore,

⇒ L B = 35 − 12

⇒ L B = 23

Therefore, LB is 23 cm.
Hence, option 1 is correct.

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