The area of the triangle can be represented by the expression 14x^5+63x^2. if the base is 7x^2, write an expression to represent its height.

Area of a triangle = 1/2 * b * h where b and h are the base and height.

Hence 1/2 * b * h = 14x^5+63x^2.

Since b = 7x^2; we have

1/2 * 7x^2 * h = 14x^5 + 63x^2.

Multiply both sides by 2 and divide both sides by 7x^2

h = 2 * (14x^5+63x^2) / 7x^2

h = (28x^5 + 126x^2) / 7x^2

h = (28/7) x^ (5-2) + (126/7) x^ (2-2)

h = 4x^3 + 18x^ (0)

h = 4x^3 + 18

The first thing you should know for this case is that the area of a triangle is given by:

A = (1/2) * (b) * (h)

Where,

b: base.

h: height.

Clearing the height we have:

h = ((2) * (A)) / (b)

Substituting the values

h = ((2) * (14x ^ 5 + 63x ^ 2)) / (7x ^ 2)

Simplifying the expression:

h = ((2) * (2x ^ 3 + 9))

h = 4x ^ 3 + 18

answer

an expression to represent its height is

h = 4x ^ 3 + 18