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
Now, we have a simplified version of the geometric shape. Let’s pick the right triangle in the next figure and apply 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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