Berdasarkan gambar di samping, garis AB∥CD. b. Jika panjang AD=16 cm dan BC=20 cm, hitunglah panjang AE dan BE.

Pertanyaan

Berdasarkan gambar di samping, garis $\style{font-size:14px}{\mathbf{AB}\boldsymbol\parallel\mathbf{CD}}$ .

b. Jika panjang $\style{font-size:14px}{\mathrm{AD}=16\;\mathrm{cm}}$ dan $\style{font-size:14px}{\mathrm{BC}=20\;\mathrm{cm}}$ , hitunglah panjang AE dan BE.

S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

panjang $\mathrm{AE}\;=12\;\mathrm{cm}$ dan panjang $\mathrm{BE}\;=\;15\;\mathrm{cm}$ .

Pembahasan

Perhatikan bahwa segitiga ABE dan segitiga DCE sebangun sebab $\mathrm{AB}\parallel\mathrm{CD}$ , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell CD over AB end cell equals cell ED over AE end cell row cell 6 over 18 end cell equals cell fraction numerator AD minus AE over denominator AE end fraction end cell row cell 6 over 18 end cell equals cell fraction numerator 16 minus AE over denominator AE end fraction end cell row cell 6 cross times AE end cell equals cell 18 open parentheses 16 minus AE close parentheses end cell row cell 6 AE end cell equals cell 288 minus 18 AE end cell row cell 6 AE plus 18 AE end cell equals 288 row cell 24 AE end cell equals 288 row AE equals cell 288 over 24 end cell row AE equals cell 12 space cm end cell end table end style$

Dan

$table attributes columnalign right center left columnspacing 0px end attributes row cell CD over AB end cell equals cell CE over BE end cell row cell 6 over 18 end cell equals cell fraction numerator 20 minus BE over denominator BE end fraction end cell row cell 6 cross times BE end cell equals cell 18 open parentheses 20 minus BE close parentheses end cell row cell 6 BE end cell equals cell 360 minus 18 BE end cell row cell 24 BE end cell equals 360 row BE equals cell 360 over 24 end cell row BE equals cell 15 space cm end cell end table$

Dengan demikian, panjang $\mathrm{AE}\;=12\;\mathrm{cm}$ dan panjang $\mathrm{BE}\;=\;15\;\mathrm{cm}$ .

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