Given the area of a triangle is 14x^2 + 15x+4 and the base is 4x+2, write the algebraic expression for the height

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