In the figure, $ABCD$ is a parallelogram, $AE \perp DC$ and $CF \perp AD$. If $AD = 6\ cm, CF = 10\ cm, AE = 8\ cm$, find $AB$.
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Given:

$ABCD$ is a parallelogram, $AE \perp DC$ and $CF \perp AD$.

$AD = 6\ cm, CF = 10\ cm, AE = 8\ cm$.

To do:

We have to find $AB$.

Solution:

We know that,

Area of a parallelogram $=$ Base $\times$ Altitude

Therefore,

Area of parallelogram $ABCD = AB \times AE$

$= AB \times 8$

$= 8AB\ cm^2$

This implies,

Altitude $CF = 10\ cm$

Area $=$ Base(AD) $\times$ Altitude(CF)

$= 6 \times 10$

$=60\ cm^2$

Therefore,

$8AB=60$

$AB=\frac{60}{8}$

$AB=7.5\ cm$

Hence, $AB = 7.5\ cm$.