Question

Teorema de Tales.

R/21            x/7

r+x=16.

Answer 1

Se a/c = b/d, podemos dizer que:

$\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a+b}{c+d}$
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$\dfrac{R}{21}=\dfrac{x}{7}$

Simplificando:

$\dfrac{R}{3}=\dfrac{x}{1}$

Então, podemos dizer que:

$\dfrac{R}{3}=\dfrac{x}{1}=\dfrac{R+x}{3+1}~~~\therefore~~~\boxed{\boxed{\dfrac{R}{3}=\dfrac{x}{1}=\dfrac{R+x}{4}}}$

Como R + x = 16:

$\dfrac{R}{3}=\dfrac{x}{1}=\dfrac{16}{4}\\\\\\\dfrac{R}{3}=x=4$
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$\dfrac{R}{3}=4\\R=4*3\\R=12\\\\x=4$