sebuah taman di sudut pekarangan rumah berbentuk segitiga siku siku dengan oanjang sisi pengikunya (2x+3)m dan (x+2)m. jika luas taman tersebut 60m². tentukan A) persamaan kuadrat yang menunjukkan luas taman tersebut B) ukuran panjang ketiga sisi taman tersebut

<p>Jawaban yang tepat adalah&nbsp;</p><ul><li>2x² + 7x - 114 = 0</li><li>Panjang ketiga sisi taman adalah 15 m, 8 m dan 17 m</li></ul><p>&nbsp;</p><p>Pembahasan :</p><p>a. L = ½ (2x + 3)(x + 2)</p><p>&nbsp; &nbsp; 60 = ½ (2x² + 7x + 6)</p><p>&nbsp; &nbsp; 120 = 2x² + 7x + 6</p><p>&nbsp; &nbsp; 2x² + 7x + 6 - 120 = 0</p><p>&nbsp; &nbsp; 2x² + 7x - 114 = 0</p><p>&nbsp;</p><p>b. Mencari panjang sisi</p><p>&nbsp; &nbsp; &nbsp;Mencari nilai x</p><p>&nbsp; &nbsp; &nbsp;2x² + 7x - 114 = 0</p><p>&nbsp; &nbsp; &nbsp;2x² + 19x - 12x - 114 = 0</p><p>&nbsp; &nbsp; &nbsp;x(2x + 19) - 6(2x + 19) = 0</p><p>&nbsp; &nbsp; &nbsp;(x - 6)(2x + 19) = 0</p><p>&nbsp; &nbsp; &nbsp;x₁ = 6 atau x₂ = -19/2</p><p>&nbsp; &nbsp; &nbsp;x = &nbsp;-19/2 tidak memenuhi syarat karena negatif, maka kita pakai x = 6</p><p>&nbsp; &nbsp; &nbsp;Panjang sisi-sisinya adalah&nbsp;</p><p>&nbsp; &nbsp; &nbsp;2x + 3 = 2(6) + 3 = 15 m</p><p>&nbsp; &nbsp; &nbsp;x + 2 = 6 + 2 = 8 m</p><p>&nbsp; &nbsp; &nbsp;Sisi miring = √(15² + 8²)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = √( 225 + 64)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = √289</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 17 m</p><p>&nbsp; &nbsp; &nbsp;Jadi Panjang ketiga sisi taman adalah 15 m, 8 m dan 17 m</p><p>&nbsp;</p><p>&nbsp; &nbsp;&nbsp;</p>