Step-by-step explanation:
l = length
w = width
l×w = 81 in²
l = 2w + 9
we can use the identity of the second equation in the first equation :
(2w + 9)×w = 81
2w² + 9w = 81
2w² + 9w - 81 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = w
a = 2
b = 9
c = -81
w = (-9 ± sqrt(9² - 4×2×-81))/(2×2) =
= (-9 ± sqrt(81 + 648))/4 =
= (-9 ± sqrt(729))/4 = (-9 ± 27)/4
w1 = (-9 + 27)/4 = 18/4 = 9/2 in
w2 = (-9 - 27)/4 = -36/4 = -9
a negative solution for a side length does not make any sense, so, width = 9/2 in is the only valid solution.
l = 2w + 9 = 2×9/2 + 9 = 9+9 = 18 in
so, the last answer option is correct.
