Question

Triunghiul dreptunghic ABC, ∡A = 90°, are cateta Ab = 6√3 cm , unde AD⊥BC, D∈ BC si ∡BAD= 30°.
a) Calculati aria triunghiului ABC
b) Aflati raportul Aria ADB/ Aria ADC.

Answer 1

2Răspuns:

Explicație pas cu pas:D=3√3cm

In Δ dreptunghic ADB  ∡BAD=30°⇒ BD=AB/2⇒   BD=3√3cm

teorema catetei

AB²=BD×BC            108=3√3BC       36=√3BC    BC=36√3/3=12√3cm

DC=BC-BD=12√3-3√3=9√3cm

AC²=DC×BC=9√3×12√3=324  ⇒AC=18cm

P=18+12√3+6√3=18+18√3=18(1+√3) cm

a)A=AB×AC/2=18×6√3/2=54√3cm²

b)Aadb=AD×BD/2

Aadc=AD×DC/2

Aadb×/Aadc=BD/DC=3√3/9√3=1/3