Kujikelezo nxantathu: ingqiqo, iimpawu, iindlela zokubona

Triangle yenye iimilo ezisisiseko zejiyometri emele ziqwempu ezintathu umgca ezidibanayo. Eli nani kwaziwa ngumphengululi eYiputa mandulo, Greece yamandulo kunye neTshayina, okunyusileyo inkoliso fomyula kunye neendlela ezisetyenziswa zizazinzulu, iinjineli kunye nabayili kude.

Iinxalenye Icandelo iphambili nxantathu zezi:

• incopho - kwindawo yonqumlo komsindo.

• Amaqela - ezidibanayo inxalenye line.

Ngokusekelwe kwezi amacandelo, ukuqulunqa ingqiqo ezifana kujikelezo unxantathu, kwindawo yayo, obhalwe kunye nezisekelwe. Ukusuka esikolweni siyazi ukuba kujikelezo kanxantathu kukho ibinzana ngamanani wamcacisela inani zonke ezintathu namacala aso. Ngelo xesha linye fomyula nokufumana eli xabiso iyaziwa abaninzi, kuxhomekeke data ekrwada ukuba abaphandi babe indlela kwimeko ethile.

1. Indlela elula yokufumana kujikelezo kanxantathu lisetyenziswa kwimeko xa amaxabiso wokwamanani baziwa kuwo omathathu amacala ayo (x, y, z), ngenxa yoko;

P = x + y + z

2. Le lokubiyela unxantathu alinganayo inokufumaneka, xa sikhumbula ukuba eli nani onke amaqela, Noko ke, njengoko bayalingana zonke engile. Ukwazi Ubude icala unxantathu umjikelezo alinganayo ibalwa ngolu hlobo lulandelayo:

P = 3gp

3. isosceles unxantathu, ngokuchaseneyo alinganayo, amacala amabini kuphela anexabiso olufanayo lwamanani, kunjalo kule meko kujikelezo ngendlela jikelele ziya kuba zezi zilandelayo:

P = 2x + y

4. Le ndlela ilandelayo iyimfuneko kwiimeko apho amaxabiso ezaziwayo lwamanani hayi onke amaqela. Umzekelo, ukuba phando data macala mabini, kwaye kananjalo eyaziwa engile therebetween, kujikelezo nxantathu ingafunyanwa ngokujonga liqela lesithathu kwaye engile eyaziwa. Kulo mzekelo, iqela lesithathu ziya kufumaneka ukusuka ifomula:

z = '2x' + 2y-2xycosβ

Ngako oko, kujikelezo kanxantathu silingana:

P = x + y + '2x' + (2y-2xycos β)

5. Kwimeko apho ubude ekuqaleni abazinikwanga ngaphezu kwesinye icala nxantathu kunye neenqobo ezaziwayo ngamanani engile ezimbini planye, kujikelezo nxantathu nga kubalwa ngokususela theorem sine:

P = x + sinβ x / (isono (180 ° -β)) + sinγ x / (isono (180 ° -γ))

6. Kukho iimeko apho ukufumana kujikelezo unxantathu besebenzisa eyaziwa parameters isangqa sibhalwe kuyo. Le fomyula yaziwa kakuhle ezininzi esikolweni:

P = 2 / r (S - indawo wesangqa, kanti r - embindini).

Ukusuka zonke ngentla kucacile ukuba ixabiso yomjikelezo unxantathu ingafumaneka ngeendlela ezininzi, ngokusekelwe kwedatha ezigcinwe uphando. Ukongeza, kukho iimeko ezizodwa embalwa, ukufumana eli xabiso. Ngoko ke, la manani achazwe sesinye neenqobo ezibaluleke kakhulu uze iimpawu nonxantathu lasekunene-yomumo.

Njengoko yaziwa, benjenjalo ukumemeza nxantathu imilo, amacala amabini kuzo zenze esinekona sasekunene. Lokubiyela unxantathu lungelo udibaniso ibinzana yamanani wakuqeqesho imilenze kunye hypotenuse. Xa kunjalo, ukuba umphandi eyaziwa data kuphela macala mabini, intsalela kungaba ibalwe kusetyenziswa theorem odumileyo kaPythagoras: Z = (x2 + y2), ukuba siyazi zombini umlenze, okanye x = (z2 - y2), ukuba siyazi ukuba hypotenuse kunye nomlenze.

Xa kunjalo, ukuba siyazi ubude hypotenuse nalowo osecaleni kwi ezimbombeni zaso, abanye amacala amabini ngu: x = z sinβ, y = z cosβ. Kulo mzekelo, kwibala unxantathu ilungelo ilingana:

P = z (cosβ + sinβ +1)

Kwakhona, a Eyonanto ibalulekileyo ukubalwa yomjikelezo ezichanekileyo (okanye alinganayo) unxantathu, oko kukuthi, oyintsobi onjalo apho onke amacala nee-engile bonke bayalingana. Ukubalwa kujikelezo unxantathu kwicala eyaziwayo akukho ngxaki, kunjalo, abaphandi asoloko eyazi ezinye iinkcukacha. Ngoko ke, ukuba radius eyaziwa wesangqa sibhalwe, kwibala unxantathu rhoqo siyinikwe:

P = 6√3r

Ukuba ukukhanya akunike ixabiso embindini wesangqa nezisekelwe, unxantathu umjikelezo alinganayo ufumaneka ngolu hlobo lulandelayo:

P = 3√3R

Iifomula kufuneka ukhumbule ukuba priment ngempumelelo practice.