Mathematics: Need with geometry. show work. just 11.

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Need with geometry. show work. just 11.

Ответ:

adriandehoyos1p3hpwc

17.01.2022

11)

when it comes to a right-triangle, having a line cutting the right-angle and perpendicular to the opposite side, like in this case, what happens is, we end up with 3 similar triangles.

a Large one, containing the other two.

a Medium one, one of the small ones.

a Small one.

so then, we can use the ratios from all these triangles, Check the picture below.

$\bf \cfrac{Large}{Small}\qquad \qquad \cfrac{x+10}{20}=\cfrac{20}{10}\implies \cfrac{x+10}{20}=2\implies x+10=40\implies \boxed{x=30} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{Small}{Medium}\qquad \qquad \cfrac{10}{y}=\cfrac{y}{x}\implies \cfrac{10}{y}=\cfrac{y}{30}\implies 300=y^2\implies \sqrt{300}=y$

$\bf \sqrt{3\cdot 100}=y\implies \sqrt{3\cdot 10^2}=y\implies \boxed{10\sqrt{3}=y} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{Medium}{Large}\qquad \qquad \cfrac{x}{z}=\cfrac{z}{x+10}\implies \cfrac{30}{z}=\cfrac{z}{30+10}\implies \cfrac{30}{z}=\cfrac{z}{40} \\\\\\ 1200=z^2\implies \sqrt{1200}=z\implies \sqrt{3\cdot 20^2}=z\implies \boxed{20\sqrt{3}=z}$

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Need with geometry. show work. just 11.

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