In the given figure, ABCD is a parallelogram. DL is perpendicular to AB and AB = 12 cm. AD = 10 cm. If the area of parallelogram is $156 c m^{2}$ then, AL = __

8 cm

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2 cm

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5 cm

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18 cm

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Solution

The correct option is A
8 cm

Area of parallelogram $= B a s e \times c o r r e s p o n d i n g a l t i t u d e$

$72 = 12 \times D L$

$D L = 6 c m$

Apply Pythagoras theorem in Triangle DLA

$A D^{2} = D L^{2} + A L^{2}$

$10^{2} = 6^{2} + A L^{2}$

$100 = 36 + A L^{2}$

$A L^{2} = 64$

$A L = 8 c m$

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Similar questions

In the given figure , ABCD is a parallelogram. DL is perpendicular to AB and AB =AD =13 cm. If the area of parallelogram is $156 c m^{2}$ then find the length of AL. [2 MARKS]

Q. In the given figure,

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is a parallelogram.

D L ⊥ A B

and

A B = 13

= A D

. If the area of parallelogram is

156 {cm}^{2}

. Then

A L

is _________.

In the given figure, ABCD is a parallelogram. DL is perpendicular to AB and AB = 12 cm. AD = 10 cm. If the area of parallelogram is $72 c m^{2}$ then, AL = __