Question

Calculati lungimile catetelor unui triunghi dreptunghic stind ca proiectile catetelor pe ipotenuza au lungimile:a)9 cm si 16 cm b)4 cm si 12cm c)15 cm si 5 cm d)x cm si 9x cm >0

Answer 1

Răspuns:

a)

BD = 9 cm

DC = 16cm

BC = BD + DC = 9 cm + 16 cm = 25 cm

AB = √(BD x BC) = √(9 x 25) = √225 = 15 cm

AC = √(DC x BC) = √(16 x 25) = √400 = 20 cm

b)

BD = 4 cm

DC = 12 cm

BC = BD + DC = 4 cm + 12 cm = 16 cm

AB = √(BD x BC) = √(4 x 16) = √64 = 8 cm

AC = √(DC x BC) = √(12 x 16) = √192 = 8√3 cm

c)

BD = 9 cm

CD = 12 cm

BC = BD + CD = 9 + 12 = 21 cm

AB = √(BD x BC) = √(9 x 21) = √189 = 3√21 cm

AC = √(CD x BC) = √(12 x 21) = √252 = 6√7 cm

d)

BD = x cm

CD = 9x cm

BC = BD + CD = x + 9x = 10x cm

AB = √(BD x BC) = √(X x 10X) = √10x² = x√10 cm

AC = √(CD x BC) = √((9X x 10X) = √90x² = 3x√10 cm

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