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Question

ABCD is a Parallelogram, A E perpendicular D C text  and  end text C F perpendicular A D If DC=16cm, AE = 8 cm and CF = 10 cm, Find AD

  1. 10.5 cm    
  2. 11.8 cm    
  3. 12.8 cm    
  4. 15.5 cm    

hintHint:

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. Here we have given ABCD is a Parallelogram, we have to find the dimension of AD. 

The correct answer is: 12.8 cm


    A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the total of all interior angles.
    A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base, which is one of its parallel sides, and height, which is the altitude measured from top to bottom, both affect the area of a parallelogram. A parallelogram's perimeter is determined by the lengths of its four sides.

    Here we have given ABCD is a Parallelogram, A E perpendicular D C text  and  end text C F perpendicular A D If DC=16cm, AE = 8 cm and CF = 10 cm.
    N o w space A B C D space i s space p a r a l l e log r a m comma space s o space o p p o s i t e space s i d e s space a r e space e q u a l comma space s o space w e space g e t colon
A B equals D C equals 16 space c m space
N o w space w e space k n o w space t h a t colon
a r e a space o f space p a r a l l e log r a m space equals space B a s e space cross times space a l t i t u d e
a r e a space o f space p a r a l l e log r a m space equals space 16 space cross times space 8
H e r e space C D space a n d space A D space a c t space a s space t h e space b a s e space a n d space A E space perpendicular space C D comma space C F space perpendicular space A D space a r e space t h e space c o r r e s p o n d i n g space a l t i t u d e s comma space s o colon
A D space equals space fraction numerator left parenthesis C D space cross times space A E right parenthesis over denominator C F end fraction
P u t t i n g space t h e space v a l u e s space i n space i t comma space w e space g e t colon
A D space equals space fraction numerator left parenthesis 16 space cross times space 8 right parenthesis over denominator 10 end fraction
A D space equals space 12.8 space c m.

    Here we used the concept of parallelogram and identified some concepts of corresponding attitudes. A parallelogram is a two-dimensional flat shape with four angles. The internal angles on either side are equal. So the dimension of AD is 12.8 cm.

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