In Figure, ABCD is a parallelogram, \(AE\perp{DC}\) and \(CF\perp{AD}\).
If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

In parallelogram ABCD, CD = AB = 16 cm [Opposite sides of a parallelogram are equal]

We know that,
Area of a parallelogram
= Base x Corresponding altitude
\(\Rightarrow \)Area of parallelogram ABCD
= CD x AE ...(i)

Also, Area of parallelogram
= Base x Corresponding altitude
\(\Rightarrow \) Area of parallelogram ABCD
= AD x CF ...(ii)

Thus, from (i) and (ii), we get,
CD x AE = AD x CF
\(\Rightarrow \) 16cm x 8cm = AD x 10cm
\(\Rightarrow \) AD = \(\frac{16cm x 8cm}{10cm} \)
\(\Rightarrow \) AD = 12.8cm
\(\therefore\) the length of AD is 12.8 cm.