Consider a parallelogram ABCD. AE is perpendicular to DC and CF is perpendicular to AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, Find AD.

A parallelogram is a quadrilateral, whose opposite sides are parallel and equal to each other.

Answer: For a parallelogram ABCD, where AE is perpendicular to DC and CF is perpendicular to AD with AB = 16 cm, AE = 8 cm and CF = 10 cm, AD is 12.8 cm.

Let's draw a diagram of parallelogram ABCD to find AD

Explanation:

Below is the diagram of parallelogram ABCD discussed in the question.

AE = 8cm (given)

CF = 10cm (given)

AB = DC = 16cm (Opposite sides of a parallelogram are equal)

Now, to calculate the value of AD

We know that,

Area of parallelogram = b × h (where b = base, h = height)

⇒ Area of ABCD = DC × AE = AD × FC

⇒ 16 × 8 = AD × 10 (By substituting all the values)

=> 128 = 10 AD

=> AD = 12.8 cm

Thus, for a parallelogram ABCD, where AE is perpendicular to DC and CF is perpendicular to AD with AB = 16 cm, AE = 8 cm and CF = 10 cm, the length of AD is 12.8 cm.