Question

one side AB of parallelogram is9cm and it's area is 54cm2. DE perpendicular to AB. if second side is is 10cm find AE​

Answer 1

Answer:

Here it is

Step-by-step explanation:

Area of a parallelogram=Base×Height

So, Height=Area of parallelogram/Base

Therefore,

DE=54cm^2/AB

=(54/9)cm

=6cm

AD^2=DE^2+AE^2 (Pythagoras Theorem)

So, AE^2=AD^2-DE^2

=>AE=√(AD^2-DE^2)

=√(10^2-6^2)

=√[(10+6)(10-6)]

[a^2-b^2=(a+b)(a-b)]

=√[16×4]

=√64

=8cm

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Answer 2

The length of AE is 8 cm.

Step-by-step explanation:

Consider the provided information.

It is given that AB  =  9 cm and area is 54 cm².

DE is perpendicular on AB, So we can say that DE is the height of parallelogram with corresponding base 'AB '.

The length of another side is 10 cm, thus AD = BC = 10 cm

The area of parallelogram = $A=Base\times Height$

Substitute the respective values.

$54=9\times DE$

$DE=6$

Hence, the length of DE is 6 cm.

Apply Pythagoras theorem in triangle AED.

$AD^2 = DE^2 + AE^2$

$10^2 = 6^2 + AE^2$

$AE^2=100-36$

$AE^2=64$

$AE=8$

Hence, the length of AE is 8 cm.

#Learn more

The diagonal of a quadrilateral is 16 cm long and the perpendicular draw to it from the opposite vertice are 5.5 cm and 6.5cm . find the area of the quadrilateral.

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