3 Tutor System
Starting just at 265/hour

# 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
$$\Rightarrow$$ 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.