Question

URGENT !!!
Fie Δ ABC dreptunghic cu ∡ A=90 si AD⊥ BC, D∈BC si stiind ca AriaABC este 486 cm² si CD/BD = 16/9

Calculati:
a) perimetrul ΔABC
b) lungimea inaltimii AD

Answer 1

CD/BD = 16/9

CD = 16k

BD = 9k

=>BC = CD + BD = 16k + 9k = 25k

T. Catetei

AB = √(BD × BC) = √(9k × 25k) = √(9 × 25×k²) =3×5×k=15k

AC = √(CD × BC) = √(16k × 25k) = √(16 × 25*k^2) =4×5×k=20k

Aria = AB×AC/2=15k×20k/2 = 15k×10k = 150k²

Aria = 486 cm²

150k² = 486

k² = 486/150 = 3,24

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k = √3,24 = 1,8

AB = 15k = 15 × 1,8 = 27 cm

AC = 20k = 20 × 1,8 = 36 cm

T.Pitagora

BC = √(AB²+AC²)=√(27²+36²) = √(729+1296) = √2025 = 45 cm

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a) P = 27+36+45 = 108

b) AD = AB × AC / BC = 27 × 36 / 45 = 21,6 cm

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