Roboguru

Diketahui titik E, F, dan G pada trapesium ABCD. Sisi FE sejajar dengan sisi AB. Jika AB = 7, DG = 8, FG = 4, GB = x, dan GE = y, maka nilai x + y adalah   "

Pertanyaan

Diketahui titik EF, dan G pada trapesium ABCD. Sisi FE sejajar dengan sisi AB. Jika AB = 7, DG = 8, FG = 4, GB = x, dan GE = y, maka nilai x + y adalah begin mathsize 14px style horizontal ellipsis end style 

"

  1. 10

  2. 11space

  3. 12space

  4. 13space

Pembahasan Soal:

  • Mendapat nilai x

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell triangle A B D tilde triangle F G D end cell row cell fraction numerator A B over denominator F G end fraction end cell equals cell fraction numerator B D over denominator G D end fraction end cell row cell 7 over 4 end cell equals cell fraction numerator 8 plus x over denominator 8 end fraction end cell row 14 equals cell 8 plus x end cell row x equals 6 end table end style 

  • Mendapat nilai y
    Tentukan panjang FD (teorema pythagoras)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F D end cell equals cell square root of 8 squared minus 4 squared end root end cell row blank equals cell square root of 64 minus 16 end root end cell row blank equals cell square root of 48 end cell row blank equals cell 4 square root of 3 end cell end table end style 

  • Menentukan AF

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 7 over 4 end cell equals cell fraction numerator A D over denominator F D end fraction end cell row cell 7 over 4 end cell equals cell fraction numerator F D plus A F over denominator 4 square root of 3 end fraction end cell row cell 7 over 4 end cell equals cell fraction numerator 4 square root of 3 plus A F over denominator 4 square root of 3 end fraction end cell row cell 7 square root of 3 end cell equals cell 4 square root of 3 plus A F end cell row cell A F end cell equals cell 3 square root of 3 end cell end table end style 

  • begin mathsize 14px style Trapesium space ABEF tilde Trapesium space FECD end style (menggunakan rumus ikan)

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F E end cell equals cell fraction numerator D C cross times A F plus F D cross times A B over denominator A F plus F D end fraction end cell row blank equals cell fraction numerator 14 cross times 3 square root of 3 plus 4 square root of 3 cross times 7 over denominator 4 square root of 3 plus 3 square root of 3 end fraction end cell row blank equals cell fraction numerator 42 square root of 3 plus 28 square root of 3 over denominator 7 square root of 3 end fraction end cell row blank equals cell fraction numerator 70 square root of 3 over denominator 7 square root of 3 end fraction end cell row blank equals 10 end table end style  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F E end cell equals cell F G plus y end cell row 10 equals cell 4 plus y end cell row y equals 6 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals cell 6 plus 6 end cell row blank equals 12 end table end style  

Maka, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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