Question

The adjacent sides ab and ad of a parallelogram abcd are 30 & 25 cm . if ae = 6.5cm find af

Answer 1

30x 6.5 -- 25 x af then, af -- 195/25 -- 7.8 cm

Answer 2

If AE = 6.5 cm, then the length of AF is 7.8 cm.

Step-by-step explanation:

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.

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