Home/ Intrebari/Q 72023
Urmator
In Process

AniDeȘcoală.ro Latest Intrebari

buburuza_cubuline
Pe: 2011-03-13T14:11:22+02:00 In: In:

problema geometrie a VII-a

ABC triunghi dreptunghic
< A = 90 grade
AD perpendicular pe BC ; D apartine lui BC
Perimetrul = 144 cm
BD/CD = 9/16
Calculati :
a) Lunghimea laturilor AB , AC , BC
b) Lungimea inaltimii AD
c) Aria triunghiului ABC

Sper ca ma puteti ajuta sa o rezolv.Multumesc anticipat.

Similare

2 raspunsuri

  1. ambri
    veteran (III)

    \rm{\frac{BD}{DC}=\frac{9}{16}\Rightarrow BD=9k; DC=16k , (k\in R_^*)\\T.h.\Rightarrow AD^2=BD\cdot DC \Rightarrow AD^2=9k\cdot16k=9\cdot16\cdot k^2\Rightarrow AD=\sqrt{9\cdot16\cdot k^2}\Rightarrow AD=3\cdot4\cdot k\Rightarrow AD=12k\\T.P. in\Delta ADB\Rightarrow AD=15k\\T.P. in \Delta ADC\Rightarrow AC=20k\\BC=9k+16k \Rightarrow BC=25k \bl}

    \rm{P = AB+AC+BC =15k+20k+25K =60k (1)\\P = 144 (2)\\(1), (2)\Rightarrow 60k=144\Rightarrow k=\frac{144}{60}\Rightarrow k= 2,4\\AB=15\cdot2,5=36cm\\AC=20\cdot2,4=48cm\\BC=25\cdot2,4=60cm\\Aria \Delta ABC =S\Rightarrow S=\frac{c_1\cdot c_2}{2}=\frac{AB\cdot AC}{2}=\frac{36\cdot48}{2}\Rightarrow S=432cm^2\bl}

  2. buburuza_cubuline

    ambri wrote: \rm{\frac{BD}{DC}=\frac{9}{16}\Rightarrow BD=9k; DC=16k , (k\in R_^*)\\T.h.\Rightarrow AD^2=BD\cdot DC \Rightarrow AD^2=9k\cdot16k=9\cdot16\cdot k^2\Rightarrow AD=\sqrt{9\cdot16\cdot k^2}\Rightarrow AD=3\cdot4\cdot k\Rightarrow AD=12k\\T.P. in\Delta ADB\Rightarrow AD=15k\\T.P. in \Delta ADC\Rightarrow AC=20k\\BC=9k+16k \Rightarrow BC=25k \bl}

    \rm{P = AB+AC+BC =15k+20k+25K =60k (1)\\P = 144 (2)\\(1), (2)\Rightarrow 60k=144\Rightarrow k=\frac{144}{60}\Rightarrow k= 2,4\\AB=15\cdot2,5=36cm\\AC=20\cdot2,4=48cm\\BC=25\cdot2,4=60cm\\Aria \Delta ABC =S\Rightarrow S=\frac{c_1\cdot c_2}{2}=\frac{AB\cdot AC}{2}=\frac{36\cdot48}{2}\Rightarrow S=432cm^2\bl}

    Nu am cuvinte de multumire,,atat de detailat,usor de urmarit.va multumesc din suflet pentru ajutor ! Incercasem tot felul de metode sa pot gasi doua relatii din care sa pot afla macar o latura..dar,acum am inteles ca incercarile mele erau in van..stiam ,simteam ca raportul e cheia ,dar din pacate solutia era departe ,mult, de mine!
    Un inceput de saptamana ,incununat de succese si multe bucurii,va doresc din suflet!

Raspunde

Raspunde