Question

The width of a rectangle is six meters less than three times its length. If the area of the rectangle is 105 square meters. what is the length

Answer 1

Answer:

length = 7 meters

Step-by-step explanation:

l = length

w = width

w = 3×l - 6

l×w = 105 m²

l×(3×l - 6) = 105

3×l² - 6×l = 105

l² - 2×l = 35

l² - 2×l - 35 = 0

solution of a squared equation is

(-b ± sqrt(b² - 4ac))/(2a)

a = 1

b = -2

c = -35

(2 ± sqrt(4 - 4×-35))/2 = (2 ± sqrt(4+140))/2 =

(2 ± sqrt(144))/2 = (2 ± 12)/2 = 1 ± 6

l1 = 1+6 = 7 meters

l2 = 1-6 = -5 meters, which did not make any sense for an actual object.

so, l = 7 meters remains.