Answer:Therefore, the dimensions of the rectangle are 14 ft by 4 ft.
Let's use variables to represent the length and width of the rectangle. We know from the problem that:Length = 3 times the width + 2
Area = 40 ft²We can use the formula for the area of a rectangle to set up an equation:Area = length x widthSubstituting in the values we have:40 = (3w + 2)wExpanding the brackets and simplifying:40 = 3w² + 2wRearranging into a quadratic equation form:3w² + 2w - 40 = 0We can solve for w using the quadratic formula:w = (-2 ± sqrt(2² - 4(3)(-40))) / (2 x 3)
w = (-2 ± sqrt(484)) / 6
w = (-2 ± 22) / 6The two possible solutions are w = 4 and w = -6.67. Since width cannot be negative, we take the positive solution: w = 4 ft.To find the length, we can use the formula we established earlier:Length = 3w + 2
Length = 3(4) + 2
Length = 14 ft