Question

In triunghiul dreptunghic ABC, m(∡A) = 90° , se cunosc BC = 30 cm si AC = 24 cm.
Calculati aria triunghiului ABC si valoarea raportului $\frac{ A_{ABD} } {A_{ACD} }$ , unde AD ⊥ BC, D ∈ (BC).

Answer 1

AB²=BC²-AC²=30²-24²=900-576=324
AB=√324
AB=18
A=AB·AC/2=18·24/2=18·12=216 aria lui ABC
AB²=DB·BC
18²=BD·30
324=BD·30
BD=324/30=10,8
CD=19,2
AD²=CD·DB=19,2·10,8=207,36
AD=√207,36
AD=14,4

Δ ADC
A=AD·DC/2=14,4·19,2/2=138,24 

Δ ADB
A=AD·DB/2=14,4·10,8/2=77,76

raportul ariilor este=77,76/138,24=0,5625