A triangle's base is 14 inches less than 2 times its height. If h represents the height in inches, and the total area of the triangle is 54 square inches, which of the following equations can be used to determine the height?
To determine the equation that can be used to find the height of the triangle, let's start by defining the variables:
Let h be the height of the triangle.
Then, the base of the triangle can be expressed as (2h - 14), since it is 14 inches less than 2 times the height.
Next, we can use the formula for the area of a triangle to set up an equation:
Area = (1/2) * base * height
Substituting the values we determined:
54 = (1/2) * (2h - 14) * h
To simplify the equation, we can multiply both sides by 2 to eliminate the fraction:
2 * 54 = (2h - 14) * h
108 = (2h - 14) * h
Expanding the equation:
108 = 2h^2 - 14h
Finally, rearranging the equation to place it in standard quadratic form:
2h^2 - 14h - 108 = 0
Therefore, the equation that can be used to determine the height is:
2h^2 - 14h - 108 = 0