# 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.

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 $cm^2$

Thus the required length of AD is 12.8 cm

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