Question

Calcule X e Y nos triângulos, nos triângulos sabendo que AD e bissetriz relativa do ângulo A

Answer 1

$a) \\ \frac{x}{12} = \frac{y}{10} \\ \\ x+y=55 \\ x=55-y \\ \\ 12y=10x \\ 12y=10(55-y) \\ 12y=550-10y \\ 12y+10y=550 \\ 22y=550 \\ y=550\div22 \\ \\\fbox{ y=25 } \\ \\ Se~~x=55-y \\x=55-25 \\\fbox{ x=30 }$~
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$b) \\ \frac{x}{12} = \frac{y}{16} \\ \\ x+y=14 \\ x=14-y \\ \\ 12y=16x \\ 12y=16(14-y) \\ 12y=224-16y \\ 12y+16y=224 \\ 28y=224 \\ y=224\div28 \\ \\\fbox{ y=8 } \\ \\ ~se~~x=14-y \\ x=14-8 \\ \\ \fbox{ x=6 }$ 
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$c) \\ \frac{x}{15} = \frac{y}{18} \\ \\ x+y=22 \\ x=22-y \\ \\ 15y=18x \\ 15y=18(22-y) \\ 15y=396-18y \\ 15y+18y=396 \\ 33y=396 \\ y=396\div33 \\ \\ \fbox{ y=12 } \\ \\ se~~x=22-y \\ x=22-12 \\ \\ \fbox{ x=10 }$