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In the adjoining figure, $$AB = 5\,\text{cm}$$, $$BC = 1\,\text{cm}$$, $$CD = DE = 4\,\text{cm}$$. Then $$AE = $$ ______ $$\text{cm}$$.
Taking the successive segments along perpendicular directions, going from $$A$$ to $$E$$ the total horizontal displacement is $$BC + DE = 1 + 4 = 5$$ and the total vertical displacement is $$AB + CD = 5 + 4 = 9$$. By the Pythagoras theorem $$AE = \sqrt{5^2 + 9^2} = \sqrt{25 + 81} = \sqrt{106}$$.
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