Math teacher doesn't know how to write questions!

A sailboat sail is triangular with a height 6 ft greater than its base. If the sail's area 20 square feet, find it's base and height

WTF?!?!

Base = 4ft
Height = 10ft

1. Write an equation. You know area equals half the base times the height so 20=1\2(bh)
2. Plug in base and height. Make the base =x and then the height equals x+6 because it is six feet greater than the base so 20=1/2x(x+6).
3. Multiply both sides by 2 so 40=x(x+6)
4. Distribute the x so 40=x^2+6x
5. Subtract 40 from both sides to get a quadratic equation (ax^2+bx+c=0) so x^2+6x-40=0
6. Factor and solve. (x+10)(x-4)=0 so x or the base equals 4 or -10. It cannot be a negative length so the base must be 4 which makes the height 10.

Let b represent the base, in feet.
Because the height is 6 ft greater than the base, (b+6) represents the height, in feet.
Since area of a triangle = (1/2)(base)(height) and the area is 20 square feet, we have

(1/2)(b)(b+6) = 20
b(b+6) = 40
b^2 + 6b = 40
b^2 + 6b - 40 = 0
(b + 10)(b - 4) = 0
b + 10 = 0 or b - 4 = 0
b = -10 or b = 4.

Discard b = -10 since the base is not negative, so b = 4.
The base is 4 feet, and the height is 4 + 6 = 10 feet.

Lord bless you today!