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Perhatikan gambar di bawah ini! Diketahui panjang  dan . Hitung panjang AB dan keliling layang-layang ABCD di atas!

Pertanyaan

Perhatikan gambar di bawah ini!

Diketahui panjang A C equals 24 space cm comma space B C equals 20 space cm dan L space A B C D equals 300 space cm squared. Hitung panjang AB dan keliling layang-layang ABCD di atas!

Pembahasan Soal:

Menentukan panjang AB

table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals cell B C end cell row blank equals cell 20 space cm end cell end table 

Menghitung panjang diagonal 2 (layang-layang)

table attributes columnalign right center left columnspacing 0px end attributes row L equals cell fraction numerator d subscript 1 cross times d subscript 2 over denominator 2 end fraction end cell row blank equals cell fraction numerator A C cross times B D over denominator 2 end fraction end cell row cell 300 space cm squared end cell equals cell fraction numerator 24 space cm cross times B D over denominator 2 end fraction end cell row cell 300 space cm squared end cell equals cell 12 space cm cross times B D end cell row cell B D end cell equals cell fraction numerator 300 space cm squared over denominator 12 space cm end fraction end cell row blank equals cell 25 space cm end cell row blank blank blank end table 

Menghitung panjang AD dan CD

table attributes columnalign right center left columnspacing 0px end attributes row cell A D end cell equals cell C D end cell row cell A O end cell equals cell C O end cell row blank equals cell 1 half cross times A C end cell row blank equals cell 1 half cross times 24 space cm end cell row blank equals cell 12 space cm end cell row cell D O end cell equals cell B D minus B O end cell row blank equals cell 25 space cm space minus open parentheses square root of B C squared minus C O squared end root close parentheses end cell row blank equals cell 25 space cm minus open parentheses square root of open parentheses 20 space cm close parentheses squared minus open parentheses 12 space cm close parentheses squared end root close parentheses end cell row blank equals cell 25 space cm minus open parentheses square root of 400 space cm squared minus 144 space cm squared end root close parentheses end cell row blank equals cell 25 space cm open parentheses square root of 256 space cm squared end root close parentheses end cell row blank equals cell 25 space cm minus 16 space cm end cell row blank equals cell 9 space cm end cell row cell A D end cell equals cell C D end cell row blank equals cell square root of D O squared plus C O squared end root end cell row blank equals cell square root of open parentheses 9 space cm close parentheses squared plus open parentheses 12 space cm close parentheses squared end root end cell row blank equals cell square root of 81 space cm squared plus 144 space cm squared end root end cell row blank equals cell square root of 225 space cm squared end root end cell row blank equals cell 15 space cm end cell end table 

Menghitung keliling layang-layang ABCD

table attributes columnalign right center left columnspacing 0px end attributes row K equals cell A D plus C D plus B C plus A B end cell row blank equals cell 15 space cm plus 15 space cm plus 20 space cm plus 20 space cm end cell row blank equals cell 70 space cm end cell end table 

Jadi, panjang A B equals 20 space cm dan keliling layang-layang A B C D equals 70 space cm.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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