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Diketahui kelompok sisi segitiga berikut: i.  ii...

Diketahui kelompok sisi segitiga berikut:

i. begin mathsize 14px style 9 space cm comma space 8 space cm comma space 6 space cm end style

ii. begin mathsize 14px style 7 space cm comma space 10 space cm comma space 12 space cm end style

iii. size 14px 5 size 14px space size 14px cm size 14px comma size 14px space size 14px 8 size 14px space size 14px cm size 14px comma size 14px space size 14px 6 size 14px space size 14px cm

Yang merupakan ukuran segitiga lancip adalah ...

  1. i dan iispace

  2. i dan iiispace

  3. ii dan iiispace

  4. i, ii, dan iiispace

Jawaban:

Jika begin mathsize 14px style a comma space b comma space dan space c end style merupakan panjang sisi-sisi suatu segitiga, dengan begin mathsize 14px style c end style adalah sisi terpanjang, maka segitiga tersebut merupakan segitiga lancip jika memenuhi

begin mathsize 14px style a squared plus b squared greater than c squared end style.

(i) Sisi terpanjang sama dengan begin mathsize 14px style 9 space cm end style, dua sisi lainnya adalah size 14px 8 size 14px space size 14px cm dansize 14px space size 14px 6 size 14px space size 14px cm. Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell open parentheses 8 space cm close parentheses squared plus open parentheses 6 space cm close parentheses squared end cell row blank equals cell 64 space cm squared plus 36 space cm squared end cell row blank equals cell 100 space cm squared end cell end table end style

serta

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell open parentheses 9 space cm close parentheses squared end cell row blank equals cell 81 space cm squared end cell end table end style

Karena

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 100 space cm squared end cell greater than cell 81 space cm squared end cell row cell a squared plus b squared end cell greater than cell c squared end cell end table end style

maka begin mathsize 14px style 9 space cm comma space 8 space cm comma space 6 space cm end style merupakan ukuran segitiga lancip.

(ii) Sisi terpanjang sama dengan size 14px 12 size 14px space size 14px cm, dua sisi lainnya adalah size 14px 7 size 14px space size 14px cm dan size 14px 10 size 14px space size 14px cm. Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell open parentheses 7 space cm close parentheses squared plus open parentheses 10 space cm close parentheses squared end cell row blank equals cell 49 space cm squared plus 100 space cm squared end cell row blank equals cell 149 space cm squared end cell end table end style

serta

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell left parenthesis 12 space cm right parenthesis squared equals 144 space cm squared end cell end table end style

Karena

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 149 space cm squared end cell greater than cell 144 space cm squared end cell row cell a squared plus b squared end cell greater than cell c squared end cell end table end style

maka begin mathsize 14px style 7 space cm comma space 10 space cm comma space 12 space cm end style merupakan ukuran segitiga lancip.

(iii) Sisi terpanjang sama dengan undefined, dua sisi lainnya adalah size 14px 5 size 14px space size 14px cm dan size 14px 6 size 14px space size 14px cm. Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared plus b squared end cell equals cell left parenthesis 5 space cm right parenthesis squared plus left parenthesis 6 space cm right parenthesis squared end cell row blank equals cell 25 space cm squared plus 36 space cm squared end cell row blank equals cell 61 space cm squared end cell end table end style

serta

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c squared end cell equals cell left parenthesis 8 space cm right parenthesis squared end cell row blank equals cell 64 space cm squared end cell end table end style

Karena

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 61 space cm squared end cell less than cell 64 space cm squared end cell row cell a squared plus b squared end cell less than cell c squared end cell end table end style

maka size 14px 5 size 14px space size 14px cm size 14px comma size 14px space size 14px 8 size 14px space size 14px cm size 14px comma size 14px space size 14px 6 size 14px space size 14px cm bukanlah ukuran segitiga lancip.

Jadi, jawaban yang tepat adalah A.

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