Let's call the base of the triangle "b" and the height "h". We know that the area of the triangle is 40 in², so:
Area = 1/2 * base * height
Plugging in the given values, we get:
40 = 1/2 * b * h
Simplifying, we get:
80 = b * h
We also know that the height is four less than six times the base, so:
h = 6b - 4
Now, we can substitute this expression for "h" into the equation we just derived for the area:
80 = b * (6b - 4)
Expanding the brackets, we get:
80 = 6b² - 4b
Rearranging, we get:
6b² - 4b - 80 = 0
Dividing both sides by 2, we get:
3b² - 2b - 40 = 0
This is a quadratic equation, which we can solve using the quadratic formula:
b = (-(-2) ± sqrt((-2)^2 - 4(3)(-40))) / 2(3)
b = (2 ± sqrt(304)) / 6
The positive solution is:
b = (2 + sqrt(304)) / 6
b ≈ 3.54
Now, we can use the equation we derived earlier to find the height:
80 = b * h
h = 80 / b
h = 80 / 3.54
h ≈ 22.6
Therefore, the base of the triangle is approximately 3.54 inches and the height is approximately 22.6 inches.