Question

Consider a parallelogram, ABCD. AE is perpendicular to DC and CF is perpendicular to AD. If AB = 16cm, AE = 8cm, and CF = 10cm, find AD.​

Answer 1

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Given:

Parallelogram ABCD

PAE = 8cm

AB = 16cm

CF = 10cm

In a parallelogram, we know that opposite sides are equal.

Therefore, CD = AB = 16cm

To find the value of AD, the base is multiplied with height.

Area of parallelogram = b x h

➠16 x 8 = AD x 10

➠ 128 = 10AD

➠ AD = 12.8cm

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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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