25. In the figure below, ABCD is a parallelogram, AE I DC and CF I AD. If AB = 16 cm,
AE = 8 cm and CF = 10 cm, find AD?
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Given:
- ABCD is a parallelogram
- FC is perpendicular kn AD
- AE is perpendicular on DC
- AE=8cm
- CF=10cm
- AB=16cm
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To find:
- Length of AD
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Solution:
When we consider base of parallelogram=AB, then height of parallelogram will be AE.
~Finding area of parallelogram
⇒ Area of ||gm=Base×Height
⇒ Area of ||gm=AB×AE
⇒ Area of ||gm=16cm×8cm
⇒ Area of ||gm=128cm²
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When we consider base of parallelogram=AD, then its height will be CF.
~Finding area of parallelogram
⇒ Area of ||gm=Base×Height
We above obtained area of ||gm=128cm², it will remain same.
⇒ 168cm²=AD×CF
⇒ 168cm²=AD×10cm
⇒ 168cm²/10cm=AD
⇒ 16.8cm=AD
So the required length of AD is 16.8cm.
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