Question

Determine x e y nas figuras a seguir.​

Answer 1

Os valores encontrados para x e y foram:

$a) x = 80 ; y = 96\\\\b) x = 20 ; y = 16$

Pelo Teorema da Bissetriz Externa, podemos estabelecer a seguinte

relação:

$a) (x + 16) / 24 = x / 20\\\\24x = 20.(x + 16)\\\\24x = 20x + 320\\\\24x - 20x = 320\\\\4x = 320 \\\\x = 320 / 4\\\\x = 80\ cm\\\\Como\ y = x + 16\ temos:\\\\y = x + 16\\\\y = 80 + 16\\\\y = 96\ cm$

$b) (4 + y) / 10 = y / 8\\\\10y = 8.(4 + y)\\\\10y = 32 + 8y\\\\10y - 8y = 32\\\\2y = 32\\\\y = 32 / 2\\\\y = 16\ cm\\\\Como\ 4 + y = x\ temos:\\\\4 + 16 = x\\\\x = 20\ cm$

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