The base of a triangle is four less than three times the height. The area of the triangle is 38 square centimeters. A=(b×h)2

Question

An expression for the base of the triangle: Response area

Equation for the area of the triangle, substituting in for the base: Response area

The first step in solving for h: Response area

Answer 1

Let's assume the base of the triangle is represented by the variable "b" and the height is represented by the variable "h".

1. An expression for the base of the triangle:
Since the base is four less than three times the height, the expression for the base would be:
b = 3h - 4

2. Equation for the area of the triangle, substituting in for the base:
The formula for the area of a triangle is A = (1/2) * base * height. Substituting in the expression for the base, the equation for the area becomes:
38 = (1/2) * (3h - 4) * h

3. The first step in solving for h:
To solve for h, we need to simplify the equation and then manipulate it to isolate the variable. First, let's distribute the (1/2) to (3h - 4):
38 = (3/2)h^2 - 2h

Now, let's combine like terms:
0 = (3/2)h^2 - 2h - 38

We have a quadratic equation in the form (Ax^2 + Bx + C = 0), so we can use the quadratic formula to solve for h:
h = (-B ± √(B^2 - 4AC)) / 2A

In our case, A = 3/2, B = -2, and C = -38. Plugging in these values, we can now solve for h.

Answer 2

What is an expression for the base of the triangle

Answer 3

An expression for the base of the triangle, as given in the problem, is:

b = 3h - 4

Answer 4

what is the first step in solving for h?

Answer 5

The first step in solving for h is to substitute the expression for the base (b = 3h - 4) into the equation for the area of the triangle (A = (1/2) * base * height).

The equation for the area becomes:
38 = (1/2) * (3h - 4) * h

We can simplify this equation by distributing the terms on the right side:

38 = (3/2)h^2 - 2h

Now we have a quadratic equation in terms of h, and we can proceed to solve it.