Home -> Solved problems -> Find the length of the black segment

### Solution

To start, let’s simplify the geometric shape following the next steps.

**Step 1:**

**Step 2:**Let \(y\) be the length of the purple segment

**Pythagoras theorem**

\[y^{2}=4^{2}+\left(3+5\right)^{2}\]

\[y^{2}=80\]

Same thing for the upper right triangle

\[y^{2}=x^{2}+3^{2}\]

\[\Rightarrow x^{2}+3^{2}=80\]

\[x^{2}=71\]

\[x>0\]

\[\huge \Rightarrow x=\sqrt{71} \]

Home -> Solved problems -> Find the length of the black segment

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

Home -> Solved problems -> Find the length of the black segment