Pertanyaan

Anggie memiliki penggaris berbentuk segitiga sama sisi. Setelah dihitung ternyata luasnya 9 3 cm 2 . Hitunglah panjang sisi segitiga tersebut! Berapa keliling segitiga tersebut?

Anggie memiliki penggaris berbentuk segitiga sama sisi. Setelah dihitung ternyata luasnya $93 cm^{2}$ . Hitunglah panjang sisi segitiga tersebut! Berapa keliling segitiga tersebut?

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Misalkan panjang sisi segitiga adalah cm. Keliling segitiga Maka Diketahui luas segitiga , maka Keliling segitiga Jadi, panjang sisi segitiga dan keliling segitiga .

Misalkan panjang sisi segitiga adalah cm.

Keliling segitiga

equals x plus x plus x equals 3 x space cm

Maka

table attributes columnalign right center left columnspacing 0px end attributes row s equals cell 1 half K end cell row blank equals cell 1 half times 3 x end cell row blank equals cell 3 over 2 x space cm end cell end table

Diketahui luas segitiga 9 square root of 3 space cm squared , maka

$table attributes columnalign right center left columnspacing 0px end attributes row Luas equals cell square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root end cell row cell 9 square root of 3 end cell equals cell square root of fraction numerator 3 x over denominator 2 end fraction left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis end root end cell row cell left parenthesis 9 square root of 3 right parenthesis squared end cell equals cell left parenthesis square root of fraction numerator 3 x over denominator 2 end fraction left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis end root right parenthesis squared end cell row cell space 243 end cell equals cell fraction numerator 3 x over denominator 2 end fraction left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis left parenthesis fraction numerator 3 x over denominator 2 end fraction minus x right parenthesis end cell row 243 equals cell fraction numerator 3 x over denominator 2 end fraction times x over 2 times x over 2 times x over 2 end cell row 243 equals cell fraction numerator 3 x to the power of 4 over denominator 16 end fraction end cell row cell fraction numerator 243 times 16 over denominator 3 end fraction end cell equals cell x to the power of 4 end cell row cell 81 times 16 end cell equals cell x to the power of 4 end cell row cell 3 to the power of 4 times 2 to the power of 4 end cell equals cell x to the power of 4 end cell row cell left parenthesis 3 times 2 right parenthesis to the power of 4 end cell equals cell x to the power of 4 space end cell row cell 6 to the power of 4 end cell equals cell x to the power of 4 end cell row cell 6 space cm end cell equals x end table$

Keliling segitiga

equals 3 x equals 3 times 6 equals 18 space cm

Jadi, panjang sisi segitiga dan keliling segitiga .