Length (L): 3w - 6
width (w): w
Area (A) = L x w
27 = (3w - 6)w
27 = 3w² - 6w
0 = 3w² - 6w - 27
0 = 3(w² - 2w - 9)
w = [tex][-(-2) +/- \sqrt{(-2)^{2} - 4(1)(-9) }]/2(1)[/tex]
= [tex][2 +/- \sqrt{(4 + 36 }]/2[/tex]
= [tex][2 +/- \sqrt{(40 }]/2[/tex]
= [tex][2 +/- 2\sqrt{(10 }]/2[/tex]
= [tex][1 +/- \sqrt{(10 }][/tex]
since width cannot be negative, disregard 1 - √10
w = 1 + √10 = 4.16
Length (L): 3w - 6 = 3(4.16) - 6 = 12.48 - 6 = 6.48
Answer: width=4.16 meters, length=6.48 meters
