Perhatikan gambar berikut! Panjang XY dan YZ adalah .... a. √13 cm dan 3√13 cm b. 2√13 cm dan 4√13 cm c. 3√13 cm dan 5√13 cm d. 4√13 cm dan 6√13 cm

<p>Jawaban: d.</p><p>&nbsp;</p><p>Ingat:</p><p>Segitiga siku-siku dengan panjang sisi tegaknya a dan b, serta panjang sisi miringnya c, berlaku rumus pythagoras:</p><p>c² = a² + b².</p><p>&nbsp;</p><p>Diketahui segitiga siku-siku XYZ dengan siku-siku di Y.</p><p>Panjang XY = 2x, YZ = 3x dan XZ 26 cm.</p><p>Maka berlaku rumus pythagoras:</p><p>&nbsp;&nbsp; &nbsp; &nbsp;XY² + YZ² = XZ²</p><p>(2x)² + (3x)² = (26)²</p><p>&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;4x² + 9x² = 676</p><p>&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;13x² = 676</p><p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; x² = 676/13</p><p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; x² = 52</p><p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; x = ± √52</p><p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; x = ± √(4 x 13)</p><p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; x = ± (√4 x √13)</p><p>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; x = ± 2√13</p><p>Karena x panjang sisi maka nilainya positif, x = 2√13 cm.</p><p>&nbsp;</p><p>Sehingga, panjang XY = 2(2√13) = 4√13 cm.</p><p>Panjang YZ = 3(2√13) = 6√13 cm.</p><p>&nbsp;</p><p>Oleh karena itu, jawaban yang benar adalah d.</p>