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Theorem 4: Diagonals of a Parallelogram Bisect Each - Other

In the given ...

Question

In the given Figure, $A B C D$ is a parallelogram, $A E ⊥ D C$ and $C F ⊥ A D$ . If $A B = 16 c m, A E = 8 c m$ and $C F = 10 c m$ , find $A D$ .

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Solution

Given, $A B = C D = 16 c m$ as opposite sides of a parallelogram are equal.
$C F = 10$ cm and $A E = 8$ cm
Now,
Area of parallelogram $=$ Base $\times$ Altitude
$\Rightarrow C D \times A E = A D \times C F$
$16 \times 8 = A D \times 10$
$A D = \frac{128}{10}$ cm
$A D = 12.8$ cm

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Similar questions

A B C D

A E ⊥ D C

C F ⊥ A D

A B = 16 c m, A E = 8 c m

C F = 10 c m

A D

A E ⊥ D C

C F ⊥ A D

A B C D

A E ⊥ D C

C F ⊥ A D .

A B = 16 c m

A E = 8 c m

C F = 10 c m,

A D .

In the given figure, ABCD is parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 6 cm, AE = 8cm and CF = 12 cm, find AD.
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