The base of a triangle is 4 less than three times the height. The area of the triangle is 38 square cm. A=b × h2 (3 points).
An expression for the base of the triangle.
a Equation for the area of the triangle:
The first step in solving for h:
To find an expression for the base of the triangle, we can start by letting the height of the triangle be represented by 'h'.
Given that the base is 4 less than three times the height, we can express the base as follows:
Base = 3h - 4
The equation for the area of the triangle is given as:
Area = (1/2) * base * height
Since the base is represented as (3h - 4) and the height is represented as 'h', the equation can be written as:
Area = (1/2) * (3h - 4) * h
To solve for h, we can set up the equation and solve for h:
38 = (1/2) * (3h - 4) * h
The first step in solving for h involves simplifying the equation by distributing (1/2) into (3h - 4):
38 = (3/2)h^2 - 2h
Now, let's solve the quadratic equation for h.
Short answer please
Expression for the base of the triangle: Base = 3h - 4
Equation for the area of the triangle: Area = (1/2) * (3h - 4) * h
First step in solving for h: Simplify the equation by distributing (1/2) into (3h - 4) and solve the resulting quadratic equation: 38 = (3/2)h^2 - 2h
To find the expression for the base of the triangle, let's denote the height as "h" and the base as "b".
From the given information, we know that the base is 4 less than three times the height. Therefore, the expression for the base can be written as:
b = 3h - 4
Next, let's find the equation for the area of the triangle. The area of a triangle is given by the formula:
Area = (1/2) * base * height
In this case, the area is given as 38 square cm. So, we can write the equation for the area as:
38 = (1/2) * b * h
Now let's move on to solving for the height. Since we need to find the value of h, we can rearrange the equation for the area to solve for h. The first step would be to multiply both sides of the equation by 2 to eliminate the fraction:
2 * 38 = b * h
76 = b * h
Now, we have an equation in terms of b and h that represents the area of the triangle. We can use this equation to solve for the height (h).
To solve this problem, let's start by finding an expression for the base of the triangle.
We are given that the base of the triangle is 4 less than three times the height. Let's set up the expression:
Let h represent the height of the triangle.
Then, the base of the triangle is (3h - 4).
Now, let's move on to finding the equation for the area of the triangle.
The formula for the area of a triangle is:
Area = (1/2) * base * height
Substituting the expressions we found earlier, we get:
Area = (1/2) * (3h - 4) * h
Next, let's find the first step in solving for h.
We are given that the area of the triangle is 38 square cm. So, we can set up the equation:
38 = (1/2) * (3h - 4) * h
Now, we have an equation that we can solve to find the value of h.