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In Fig. 9.15, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Q : 1       In Fig. \small 9.15, ABCD is a parallelogram, \small AE\perp DC and \small CF\perp AD. If \small AB=16\hspace{1mm}cm\small AE=8\hspace{1mm}cm  and \small CF=10\hspace{1mm}cm, find AD.

            

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M manish


We have,
AE \perp DC and CF \perp AD
AB = 16 cm, AE = 8 cm and CF = 10 cm

Since ABCD is a parallelogram,
therefore, AB = DC = 16 cm
We know that, area of parallelogram (ABCD) = base . height
                                                                        = CD \times AE  = (16 \times 8 ) cm^2
SInce,  CF \perp AD
therefore area of parallelogram  = AD \times CF = 128 cm^2
                                                   = AD = 128/10 
                                                   = AD = 12.8 cm                           

Thus the required length of AD is 12.8 cm        

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