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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