Question

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Answer 1

Răspuns:

1. d) 14 cm

2. c) 45°

3. a) 4cm²

Explicație pas cu pas:

1. BD = 7 cm, CD = 4 cm => BC = BD – CD =

BC = 7 cm – 4 cm = 3 cm

CE = 9 cm, CD = 4 cm => DE = CE – CD

DE = 9 cm – 4 cm = 5 cm

AB = 2cm, (BC = 3 cm, CD= 4cm, BD=BC+CD=3+4=7cm) BD=7cm, DE=5cm =>

=>AE=AB+BC+CD+DE=AB+BD+DE

AE=2cm+7cm+5cm=14cm —>d)14 cm

2. 180°-55°=2x+35° <=> 125°=2x+35° <=> 2x=125°-35° <=> 2x=90°/:2 => x= 45° —>c)

3.∆ABC isoscel => AB = AC=4cm

∡B = ∡C = 75°

∡A+∡B+∡C=180° = ∡A + 2•75° = 180°

∡A+150°=180° => ∡A=180°–150°=30°

∡BAC=∡A=30°

sin(∡BAC)=sin30°=1/2

Aria ∆ABC = [AB • AC • sin(∡BAC)]/2

Aria ∆ABC = (4•4• 1/2)/2=16/2/2=8/2

Aria ∆ABC = 4 cm² –> a) 4 cm²