Sebuah taman berbentuk trapesium sama kaki dengan panjang sisi-sisi sejajarnya (x+2) dan (2x+6) . Jika jarak kedua garis sejajar adalah x dan luas taman adalah 128 m 2 , tentukan keliling taman tersebut!

<p>Diketahui :</p><ul><li>a = (x + 2) m</li><li>b = (2x + 6) m</li><li>t = x</li><li>L = 128 m²</li></ul><p>&nbsp;</p><p>Ditanya :</p><p>Keliling taman (K)?</p><p>&nbsp;</p><p>Pembahasan :</p><p>L = ((a + b) . t)/2</p><p>128 = ((x + 2 + 2x + 6) . x) / 2</p><p>&nbsp;128 = ((3x + 8).x)/2</p><p>256 = 3x² + 8x</p><p>3x² + 8x - 256 = 0</p><p>3x² - 24x + 32x - 256 = 0</p><p>3x(x - 8) + 32(x - 8) = 0</p><p>(3x + 32)(x - 8) = 0</p><p>x = -32/3 atau x = 8</p><p>x = -32/3 tidak memenuhi syarat karena negatif</p><p>Kita ambil x = 8 sehingga :</p><p>a = 8 + 2 = 10 m</p><p>b = 2(8) + 6 = 16 + 6 = 22 m</p><p>tinggi (t) = 8 m</p><p><br>Sisi miring = √(t² + ((b-a)/2)²)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= √(8² + ((22-10)/2)²)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= √(8²+ 6²)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=√(64+ 36)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= √100</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 10 m</p><p>Keliling = a + b + 2 x sisi miring</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= 10 + 22 + 2 x 10</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= <strong>44 m</strong></p><p>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p>