width (w) = w
Length (L) = 3w - 10
Area (A) = L x w
77 = (3w - 10)w
77 = 3w² - 10w
0 = 3w² - 10w - 77
0 = 3w² - 21w + 11w - 77
0 = 3w(w - 7) + 11(w - 7)
0 = (3w + 11)(w - 7)
0 = 3w + 11, 0 = w - 7
w = [tex] \frac{-11}{3} [/tex], w = 7 (width cannot be negative!)
w = 7
Length (L) = 3w - 10 = 3(7) - 10 = 21 - 10 = 11
Answer: width = 7 ft, Length = 11 ft
