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Introduction

In the follow...

Question

In the following 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 $156 c m^{2}$ . Find $A L$ .

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Solution

The correct option is C $5$ cm
We have
Area $= 156 c m^{2}$
$∴ b \times h = 156$
$∴ A B \times D L = 156$
So, $D L = \frac{156}{A B} = \frac{156}{13} = 12$ cm

In right angled $Δ A D L$ , we have
$A D^{2} = D L^{2} + L A^{2}$ ...by Pythoagoras theorem
$A L^{2} = A D^{2} - D L^{2}$
$= 13^{2} - 12^{2}$
$= 169 - 144 = 25$
$∴ A L = \sqrt{25} = 5$ cm

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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, AL = ____.

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 = __

Q. In the given figure, ABCD is a parallelogram of area

1470 c m^{2}

D L ⊥ A B

and

B M ⊥ A B

. If

A B = 35

cm and

A D = 49

cm, find DL and BM.

D L

and

B M

are the height on sides

A B

and

A D

respectively of parallelogram

A B C D

figure. If the area of the parallelogram is

1470 c m^{2}

A B = 35 c m

and

A D = 49 c m

, find the length of

B M

and

D L

Question 6

DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is 1470 ${c m}^{2}$ , AB = 35 cm and AD = 49 cm, find the length of BM and DL.

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In the following figure, □ABCD is a parallelogram. DL⊥AB and AB=13 cm =AD. If the area of parallelogram is 156cm2. Find AL.

The correct option is C 5 cmWe have Area =156 cm2∴b×h=156∴AB×DL=156So, DL=156AB=15613=12 cmIn right angled ΔADL, we haveAD2=DL2+LA2 ...by Pythoagoras theoremAL2=AD2−DL2=132−122=169−144=25∴AL=√25=5 cm

In the following 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 $156 c m^{2}$ . Find $A L$ .