in the given figure abcd is a parallelogram, ap is perpendicular to dc and cq is perpendicular to ad. if ab=10cm, ad=8cmand ap=8cm then cq=

Answer :

We have a parallelogram ABCD  , Here AP $\perp$ DC  and CQ $\perp$ AD  . And

AB  =  10 cm  ,  AD  =  8 cm and AP  =  8 cm 

From given information we form our figure , As  :

And we know Area of parallelogram  =  (  Base ) ( Height  )

So, We take base =  DC  , and we know DC  =  AB  =  10 cm  (  In parallelogram opposite side equal in length )

And Height =  AP =  8 cm , As given AP $\perp$ DC , So 

Area of ABCD  =  10  $\times$  8  =  80 cm²  ---------------- ( 1 )

Now , We take base =  AD  , and we know AD  =  8 cm  (  As given  )

And Height =  CQ =  h cm , As given CQ $\perp$ AD , So 

Area of ABCD  =  8  $\times$  h  =  8h cm²   ---------------- ( 2 )

Now we equation equation 1 and 2 , and get

8h  = 80

h  =  10

So,

CQ  =  10 cm  ( Ans )