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.
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
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