Question

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

Answer 1

Answer:

We have, AE ⊥ DC and AB = 16 cm

∵ AB = CD [Opposite sides of parallelogram]

∴ CD = 16 cm

Now, area of parallelogram ABCD = CD x AE

= (16 x 8) cm2 = 128 cm2 [∵ AE = 8 cm]

Since, CF ⊥ AD

∴ Area of parallelogram ABCD = AD x CF

⇒ AD x CF = 128 cm

⇒ AD x 10 cm = 128 cm2 [∵ CF= 10 cm]

⇒ AD = 128/10 cm = 12.8 cm 10

Thus, the required length of AD is 12.8 cm

Answer 2

Answer:

AD = 12.8cm

Step-by-step explanation:

AB = CD------------ (opposite sides of a parallelogram)

16cm = CD

Area of ║°gram = base x height

                          = AE x CD

                          = 8 x 16

                           = 128cm²  

Area of ║°gram = base x height

                   128 = AD x CF

                   128 = AD x 10

             12.8cm = AD

Therefore, the length of AD is 12.8cm.