Proving Similarity in the figure DEFG is a square. Prove the following: DE=sqrt(AD*EB) Given: The given figure is, 12210202691.jpg

Approach:
All the sides of a square are equal in length.
Calculation:
It is proved that,
AD * EB = DG * FE(1)
In the figure DEFG is a square, thus, DG and IE can be replaced by DE as they all are sides of a square and equal in length.
Substitute DE for DG and FE in equation (1).
AD * EB = DE * DE
${\displaystyle {\left(DE\right)}^2=AD\cdot EB}$
${\displaystyle DE=\sqrt{AD\cdot EB}}$
Therefore, it is proved that ${\displaystyle DE=\sqrt{AD\cdot EB}}$.
Conclusion:
Hence, it is proved that ${\displaystyle DE=\sqrt{AD\cdot EB}}$.