Given: - The length of the rectangle is 12 yards less than 3 times its width.
The area of the rectangle is 180 square yards. Let: - Width of the rectangle = w yards - Length of the rectangle = 3ω – 12 yards The formula for the area of a rectangle is: Area = length × width
Given that the area is 180 square yards, we can write the equation as: 180 = (3w - 12) * w
Solve for w : 180 = 3w ^ 2 - 12w 3w ^ 2 - 12w - 180 = 0 Divide the entire equation by 3 to simplify: w ^ 2 - 4w - 60 = 0 Factor the quadratic equation: (w - 10)(w + 6) = 0 So, the possible values for w are: - w = 10 (ignoring negative value as width
cannot be negative) - w = - 6
(not a valid solution as width cannot be negative)
Therefore, the width of the rectangle is 10 yards. Find the
length: Length = 3w – 12 = 3(10) – 12 = 30 - 1: Therefore, the length of the rectangle is 18 yards.
