If the area of a triangle is 110 square units and the base is 2x+12 and the height is x+5, what is the numerical base and height?
.5(2x+12)(X+5) = 110
5,-16
To find the numerical values of the base and height of the triangle, we need to solve the equation for the area of a triangle.
The formula for the area of a triangle is given by:
Area = (1/2) * base * height
Given that the area of the triangle is 110 square units, we can write the equation as:
110 = (1/2) * (2x + 12) * (x + 5)
To solve this equation, we can first simplify it by distributing the factors:
110 = (x + 6) * (x + 5)
Now, we can expand the equation:
110 = x^2 + 5x + 6x + 30
Combining like terms:
110 = x^2 + 11x + 30
Rearranging the equation to make it a quadratic equation:
x^2 + 11x + 30 - 110 = 0
x^2 + 11x - 80 = 0
Now, we can factorize the quadratic equation:
(x + 16)(x - 5) = 0
Setting each factor equal to zero:
x + 16 = 0 or x - 5 = 0
Solving for x, we get two possible values:
x = -16 or x = 5
Since the dimension of length cannot be negative, we reject the value x = -16.
Therefore, the numerical value of the base (2x + 12) and height (x + 5) of the triangle is:
Base = 2(5) + 12 = 10 + 12 = 22 units
Height = 5 + 5 = 10 units