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
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
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.
What is an expression for the base of the triangle
An expression for the base of the triangle, as given in the problem, is:
b = 3h - 4
what is the first step in solving for h?
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.
An expression for the base of the triangle can be represented as follows:
Base = 3h - 4
To find the equation for the area of the triangle, we substitute the expression for the base into the formula for the area (A = 1/2 * base * height):
A = (3h - 4) * h = 38
The first step in solving for h would be to set up the equation and simplify it:
3h^2 - 4h - 38 = 0
To find the expression for the base of the triangle, we are given that the base is four less than three times the height. Let's denote the height as 'h' and the base as 'b'.
We can express the base as: b = 3h - 4.
To find the equation for the area of the triangle, we use the formula A = (b * h) / 2, where A represents the area.
Substituting the expression for the base, we get: A = ((3h - 4) * h) / 2.
Now, let's move on to solving for the height (h).
The first step in solving for h is to set up the equation based on the given information. We are told that the area of the triangle is 38 square centimeters. So, we can set up the equation as follows:
((3h - 4) * h) / 2 = 38.
Now, we can proceed to solve for h by simplifying and rearranging this equation.