Question

1. In Fig. 9.15, ABCD is a parallelogram, AE IDC
and CF I AD. If AB = 16 cm, AE = 8 cm and
CF= 10 cm, find AD.
2
If EEG and Hare respectively the mid-points of​

Answer 1

Explanation:

1) AB = CD (Opposite sides of parallelogram)

CD = 16cm

ar( ABCD ) with AB as base

=AB*AE = 16*8cm^2

ar( ABCD ) with AD as base

=AD*CF = AD*10cm^2

AD*10 = 16*8

AD = 16*8/10

AD = 64/5

AD = 12.8cm

Answer 2

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 :-

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

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