Final answer:
To find the base and height of the triangle, set up an equation using the area formula and solve the quadratic equation. The height of the triangle is 6 inches, and the base is 22 inches.
Step-by-step explanation:
To find the base and height of the triangle, let's assign variables to them. Let's say the height of the triangle is h. According to the problem, the base of the triangle is 10 inches more than 2 times the height, so the base can be represented as 2h + 10.
The formula for the area of a triangle is (1/2) * base * height. The problem states that the area is 104 square inches, so we can set up the equation (1/2) * (2h + 10) * h = 104.
Simplifying the equation, we get (2h^2 + 10h) / 2 = 104. Multiply both sides by 2 to eliminate the fraction, and we have 2h^2 + 10h = 208. Rearranging the equation, we have 2h^2 + 10h - 208 = 0.
Now we can solve the quadratic equation using factoring, completing the square, or the quadratic formula. The solutions for h will give us the height of the triangle. Once we find the height, we can substitute it back into the equation 2h + 10 to find the base of the triangle.
After solving the quadratic equation, we find that h has two solutions, h = -16 and h = 6. The height of the triangle cannot be negative, so the height is 6 inches. Substituting this into the equation 2h + 10, we get the base as 2(6) + 10 = 22 inches.