By definition, the area of the triangle is given by:
A = (1/2) * (b) * (h)
Where,
b: base.
h: height.
Clearing the height we have:
h = (2 * A) / (b)
Substituting:
h = (2 * (14x ^ 2 + 15x + 4)) / ((4x + 2))
h = (14x ^ 2 + 15x + 4) / (2x + 1)
Making the division of polynomials we have:
h = 7x + 4
Answer:
the algebraic expression for the height is:
h = 7x + 4