Final answer:
To find the length of the banner's base, substitute the given information into the formula for the area of a triangle and solve for the base length. The length of the banner's base is 20 feet.
Step-by-step explanation:
To find the length of the banner's base, we can use the given information and the formula for the area of a triangle: 1/2 x base x height.
Let's assume the base length of the triangle is 'x'. The height of the triangle is 10 feet less than twice its base length, so it can be represented as '2x - 10'. Now, we can substitute these values into the formula for the area of the triangle: 1/2 x x x (2x - 10) = 150.
Simplifying the equation, we get x(2x - 10) = 300. Expanding and rearranging the equation, we have 2x^2 - 10x - 300 = 0. Solving this quadratic equation using factoring or the quadratic formula, we find that x = 20 or x = -7.5. Since we are dealing with a length, we discard the negative value.
Therefore, the length of the banner's base is 20 feet.