Question

Determine X e Y nas figuras

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Answer 1

a)

${y}^{2} = {(\sqrt{5})}^{2} + {x}^{2} \\ {y}^{2} = 5 + {x}^{2} \\ {y}^{2} - {x}^{2} = 5$

$y = \sqrt{5}x$

${( \sqrt{5}x)}^{2} - {x}^{2} = 5 \\ 5 {x}^{2} - {x}^{2} = 5 \\ 4 {x}^{2} = 5$

${x}^{2} = \frac{5}{4} \\ x = \sqrt{\frac{5}{4}}$

$x = \frac{ \sqrt{5} }{2}$

$y = \sqrt{5}x \\ y = \sqrt{5}. \frac{ \sqrt{5} }{2} = \frac{5}{2}$

b)

${3}^{2}=(x + 2).2 \\ 2x + 4 = 9 \\ 2x = 9 - 4$

$2x = 5 \\ x = \frac{5}{2} \\ x = 2,5$

${y}^{2} =( 2,5 + 2).2,5 \\ {y}^{2} =4,5.2,5 \\ y = \sqrt{11,25} =3,35$