Question

The adjacent Sides AB and AD of a parallelogram ABCD are 30 cm and 25 cm respectively. If AE = 6.5 cm, Find AF

Answer 1

It is given that,

In parallelogram ABCD,

AB = 30 cm

AD = 25 cm

AE = 6.5 cm ….. [the perpendicular height from vertex A on CD (as shown in the figure attached below)]

Since in a parallelogram, the opposite facing sides are equal in length .

∴ AD = BC = 25 cm and AB = CD = 30 cm ….. (i)

Also, from the figure, AF is another perpendicular height from vertex A on BC.

Now, we know that the formula for the area of the parallelogram is given by

Area = base * height

Since here we have two perpendicular heights for the parallelogram ABCD then based on the above formula we can write,

CD * AE = BC * AF

⇒ 30 * 6.5 = 25 * AF ….. [substituting the value of CD & BC from (i) and AE is given]  

⇒ AF = 195/25

⇒ AF = 7.8 cm

Thus, the perpendicular height AF is 7.8 cm.