Question

The base of a triangle is 18 inches longer than twice the length of its​ altitude, x. Write a polynomial that represents the area of the triangle?

word problem

Answer 1

See a solution process below:

Explanation:

The formula for the area of a triangle is:

`A = 1/2bh`

Where:

`A` is the Area, what we would be solving for.

`b` is the base of the triangle.

`h` is the height or altitude of the triangle.

We know from the problem the altitude is: `x`

We know from the problem the base is: `2x + 18`

Substituting and simplifying gives;

`A = 1/2(2x + 18)x`

`A = 1/2(2x^2 + 18x)`

`A = (2x^2 + 18x)/2`

`A = (2x^2)/2 + (18x)/2`

`A = x^2 + 9x`