If figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm, and CF = 10 cm, Find AD.
Question:

If figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8 cm, and CF = 10 cm, Find AD.

Solution:

Given that,

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

We know that,

Area of parallelogram = Base × Corresponding altitude

Area of parallelogram ABCD = CD × AE = AD × CF

16 cm × cm = AD × 10 cm

$\mathrm{AD}=\frac{16 \times 8}{10} \mathrm{~cm}=12.8 \mathrm{~cm}$

Thus, The length of AD is 12.8 cm.