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
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
For the base of the triangle, let's call it "b", we are given that it is four less than three times the height, so we can write it as:
b = 3h - 4
Now, let's substitute the value of the base in the formula for the area of the triangle:
Area = (b * h) / 2
Area = ((3h - 4) * h) / 2
To solve for h, let's first distribute the multiplication:
Area = (3h^2 - 4h) / 2
Now, let's rearrange the equation to isolate h:
2 * Area = 3h^2 - 4h
Rearranging the equation further:
3h^2 - 4h - 2 * Area = 0
Now, we have a quadratic equation that we can solve using the quadratic formula:
h = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case:
a = 3, b = -4, c = -2 * Area
Solving for h using the quadratic formula will give us the two possible values for the height.
whats the resposes for the blank
For the equation for the area of the triangle, substituting in for the base, the response should be:
Area = ((3h - 4) * h) / 2
And for the first step in solving for h, the response should be:
2 * Area = 3h^2 - 4h - 2 * Area = 0
what about the first one?
Apologies for the oversight. For the first step in solving for h, the response should be:
b = 3h - 4
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
pls
I apologize for the confusion. Here are the correct responses:
For the base of the triangle: Let's call it "b".
Equation for the area of the triangle, substituting in for the base:
Area = (b * h) / 2
Substituting the value of the base into the equation:
Area = ((3h - 4) * h) / 2
The first step in solving for h:
To solve for h, we need to rearrange the equation:
2 * Area = (3h - 4) * h
I apologize for any confusion caused by the incorrect responses before.
i dont have that option for the first one
Apologies for the confusion. Here are the correct responses:
For the first blank, the correct response is:
For the base of the triangle: Let's call it "b".
For the equation for the area of the triangle, substituting in for the base, the correct response is:
Area = (b * h) / 2
And for the first step in solving for h, the correct response is:
b = 3h - 4
To solve this problem, let's start by setting up the equation for the area of a triangle. The formula for the area of a triangle is:
A = (base * height) / 2
Given that the area of the triangle is 38 square centimeters, we can write:
38 = (base * height) / 2
Now, let's substitute the expression for the base given in the problem. The problem states that the base of the triangle is four less than three times the height. So, we can write:
base = 3h - 4
Substituting this into our equation for the area, we have:
38 = ((3h - 4) * height) / 2
To solve for the height (h), we will need to rearrange the equation. Multiplying both sides of the equation by 2, we have:
76 = (3h - 4) * height
Expanding the right side of the equation, we get:
76 = 3h * height - 4 * height
Now, let's simplify further. We can distribute the 3h to each term inside the parentheses:
76 = 3h^2 - 4h
Rearranging the equation, we have:
3h^2 - 4h - 76 = 0
This is a quadratic equation that can be solved using factoring, completing the square, or using the quadratic formula. Once we find the values of h, we can substitute them back into the equation for the base to find the corresponding values.