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If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.

Answer :

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.

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