Yuav ua li cas mus nrhiav tau ntawm lub perimeter ntawm daim duab peb sab?

Yuav ua li cas mus nrhiav tau ntawm lub perimeter ntawm daim duab peb sab? Yog li ntawd, lo lus nug twb nug peb txhua tus, nyob rau hauv tsev kawm ntawv. Wb sim nco ntsoov txhua yam uas peb paub txog qhov no amazing daim duab, raws li zoo raws li cov lus teb rau lo lus nug.

Lo lus teb rau lo lus nug ntawm yuav ua li cas nrhiav tau ntawm lub perimeter ntawm daim duab peb sab yog feem ntau yooj yim heev - nws yuav siv sij hawm xwb-cia li ua raws li cov txheej txheem ntawm ntxiv ntawm cov lengths ntawm tag nrho nws cov sab. Txawm li cas los, muaj ib tug ob peb yam yooj yim txoj kev tsis paub hais tias muaj nuj nqis.

Lub tswv yim

Nyob rau hauv cov ntaub ntawv uas, yog hais tias tus voos kheej-kheej (r) ntawm lub vajvoog uas yog inscribed nyob rau hauv ib tug daim duab peb sab, thiab nws cheeb tsam (S) yog lub npe hu, cov lus teb rau cov nqe lus nug ntawm yuav ua li cas nrhiav tau ntawm lub perimeter ntawm daim duab peb sab yog haum yooj yim. Ua li no, koj yuav tau siv li ib txwm mis:

P = 2s / r

Yog hais tias ob ces kaum paub, piv txwv li, α thiab β, uas yog nyob ib sab mus rau sab nws tus kheej thiab sab ntev, tus puag ncig yuav pom siv ib tug heev, heev nrov mis uas yog:

sinβ ∙ ib tug / (kev txhaum (180 ° - β - α)) + sinα ∙ ib tug / (kev txhaum (180 ° - β - α)) + ib

Yog hais tias koj paub qhov ntev ntawm lub nyob ib sab sab thiab lub kaum sab xis β, uas yog nruab nrab ntawm lawv, nyob rau hauv thiaj li yuav nrhiav tau cov perimeter, nws yuav tsum tau siv lub theorem ntawm cosines. Lub puag ncig yog xam raws li nram no:

P = b + ib + √ (B2 + a2 - 2 ∙ b ∙ thiab ∙ cosβ),

qhov twg a2 thiab B2 yog cov plaub fab ntawm lub lengths ntawm ib sab sab. Radical qhia - yog qhov ntev ntawm ib tug thib peb tog neeg uas yog tsis paub, cim los ntawm cov cosine theorem.

Yog hais tias koj tsis paub yuav ua li cas nrhiav tau cov puag ncig ntawm ib tug ceskaum daim duab peb sab, nyob ntawm no, nyob rau hauv qhov tseeb, tsis muaj big deal. Xam nws siv cov mis:

P = b + 2a,

qhov twg b - hauv paus ntawm lub daim duab peb sab, thiab - nws sab.

Yuav kom nrhiav tau ntawm lub perimeter ntawm ib tug equilateral daim duab peb sab yuav tsum tau siv ib tug yooj yim mis:

R = 3a,

thiab nyob qhov twg - qhov ntev ntawm lub sab.

Yuav ua li cas mus nrhiav tau ntawm lub perimeter ntawm daim duab peb sab yog hais tias peb paub tsuas yog tus radii ntawm lub voj voog piav txog nws los yog nkag mus rau hauv nws? Yog hais tias ib tug daim duab peb sab yog equilateral, ces nws yuav tsum tau thov cov mis:

P = 3R√3 = 6r√3,

qhov twg R thiab r yog radii ntawm lub circumscribed thiab inscribed vajvoog feem.

Yog hais tias ib tug daim duab peb sab yog ceskaum, ces cov mis yog muaj feem xyuam rau nws:

P = 2R (sinβ + 2sinα),

qhov twg α - yog lub kaum sab xis uas yog lus dag nyob puag, thiab β - lub kaum sab xis uas yog opposite rau lub hauv paus.

Feem ntau, yuav kom daws tau xyuam xim teeb meem yuav tsum tau sib sib zog nqus tsom xam thiab kev muaj peev xwm mus nrhiav thiab tso saib qhov yuav tsum tau cov qauv, uas, raws li muaj ntau yam paub, yog nej ib tug yooj yim txoj hauj lwm. Hos ib txhia cov teeb meem yuav daws tau nrog ib tug hluas mis.

Cia peb xav txog cov mis uas yog lub hauv paus rau teb rau lo lus nug ntawm yuav ua li cas nrhiav tau ntawm lub perimeter ntawm daim duab peb sab, nyob rau hauv kev sib raug zoo mus rau ib tug ntau yam ntawm hom ntawm cov vajvoos peb sab.

Ntawm cov hoob kawm, lub ntsiab cai rau kev nrhiav lub perimeter ntawm lub daim duab peb sab - tsab ntawv no yog: nws yuav tsum tau mus rau nteg cia qhov ntev ntawm nws cov sab nyob rau hauv tsim nyog mis rau nrhiav ntawm lub perimeter ntawm daim duab peb sab:

P = b + ib + c,

qhov twg b, ib tug thiab - ib tug ntev ntawm sab ntawm ib lub duab peb sab, thiab P - perimeter ntawm lub daim duab peb sab.

Muaj ntau ntau tshwj xeeb no ntawm lub mis. Piv txwv koj qhov teeb meem yog formulated raws li nram no: "yuav ua li cas nrhiav tau ntawm lub perimeter ntawm ib txoj cai daim duab peb sab" Nyob rau hauv cov ntaub ntawv no, koj yuav tsum tau siv cov nram qab no mis:

P = b + ib + √ (B2 + a2)

Nyob rau hauv cov mis no, ib tug thiab b yog cov lengths ntawm ob txhais ceg tam sim ntawd txoj cai daim duab peb sab. Ib qho yooj yim mus twv hais tias es tsis txhob ntawm ib sab (hypotenuse) yog siv qhia muab tau los ntawm lub theorem ntawm tus poj tus paub txog antiquity - Pythagoras.

Yog hais tias koj xav kom daws tau qhov teeb meem, nyob qhov twg lub duab peb ceg yog zoo sib xws, ces nws yuav muaj kuab siv tsab ntawv no: tus piv ntawm cov perimeters ntawm cov coj coefficient ntawm kev zoo sib thooj. Cia hais tias koj muaj ob zoo xws li cov duab peb ceg - ΔABC thiab ΔA1B1C1. Ces mus nrhiav cov kev zoo sib thooj tseem ceeb rau tus muab faib rau cov puag ncig ΔABC ΔA1B1C1 perimeter.

Nyob rau hauv xaus, nws yuav tsum tau muab sau tseg hais tias lub perimeter ntawm lub daim duab peb sab yuav pom siv ntau yam kev kawm, nyob ntawm seb qhov cov ntaub ntawv uas koj muaj. Nws yuav tsum tau ntxiv hais tias muaj tej yam tshwj xeeb raug rau txoj cai-angled cov vajvoos peb sab.