## Determine the length \(x\) of the blue segment

Home -> Solved problems -> We have two squares, determine the value of x

### Solution

Let’s add sections like it’s shown in the next figure

We have two squares \(\square A B C D \) and \(\square M N G F \)

\[\begin{gathered}
\Delta F C G \;is\; a\; Right \;Triangle\\\\
By\;Pythagoras\;theorem\\\\
F G^{2}=C F^{2}+C G^{2}\\\\
F G=\sqrt{4^{2}+\left(\frac{4 x}{7}\right)^{2}}\\\\
F G=\sqrt{16+\frac{16 x^{2}}{49}}=N G
\end{gathered}
\]

Home -> Solved problems -> We have two squares, determine the value of x

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Why does the number \(98\) disappear when writing the decimal expansion of \(\frac{1}{9801}\) ?