Question

If Fig. 15.26, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB=16 cm, AE=8 cm and CF=10 cm, find AD.

Answer 1

Given : ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. AB = 16 cm, AE = 8 cm and CF = 10 cm.

In  parallelogram ABCD ,  

AB = CD = 16 cm (Opposite sides of a parallelogram)

CF = 10 cm and AE = 8 cm

We know that,

Area of parallelogram = Base × Altitude

Area of parallelogram ABCD  with altitude AE = DC × AE

Area of parallelogram ABCD = 16 × 8  

[AB = DC = 16 cm (opposite sides of a parallelogram are equal]

Area of parallelogram ABCD = 128 cm²

Area of parallelogram ABCD with altitude CF = AD  × CF

128 = AD × 10

AD = 128/10 cm

AD = 12.8 cm

Hence, the value of AD is 12.8 cm.

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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.

We have :-

• AE ⊥ DC

• AB = 16 cm

• ∵ AB = CD [Opposite sides of parallelogram]

• ∴ CD = 16 cm

Now, area of parallelogram ABCD

= CD x AE

= (16 x 8)${cm}^{2}$

= 128 ${cm}^{2}$ [∵ AE = 8 cm]

_________

• Since, CF ⊥ AD

∴ Area of parallelogram ABCD

= AD x CF

⇒ AD x CF = 128 cm

⇒ AD x 10 cm = 128 ${cm}^{2}$ [∵ CF= 10 cm]

⇒ AD =$\dfrac{128}{10}$ cm

= 12.8 cm

Thus, the required length of AD is 12.8 cm