the base of a triangle is 4 less than 3 times the height . the area of the triangle is 38suare cm. a+bxh/2
an expression for the base of the triangle _
equation for the area of the triangle_
first step in solving for h_
To find an expression for the base of the triangle, let's denote the base as b and the height as h.
According to the given information, the base is 4 less than 3 times the height. So we can write the expression for the base as:
b = 3h - 4
The equation for the area of a triangle is given by the formula A = (1/2)bh, where A is the area, b is the base, and h is the height.
In this case, we are given that the area of the triangle is 38 square cm. So we can write the equation for the area as:
38 = (1/2)(b)(h)
The first step in solving for h would be to substitute the expression for the base (3h - 4) into the area equation:
38 = (1/2)(3h - 4)(h)
can you explain
Sure! Let's break down the problem step by step.
1. We are given that the base of the triangle is 4 less than 3 times the height. So, we can represent the base as b and the height as h.
The expression for the base can be written as:
b = 3h - 4
2. The formula for finding the area of a triangle is A = (1/2)bh, where A is the area, b is the base, and h is the height.
We are given that the area of the triangle is 38 square cm. So, we can write the equation for the area as:
38 = (1/2)bh
3. To solve for the height, we need to eliminate the base from the equation. We can substitute the expression for the base from step 1 into the area equation from step 2:
38 = (1/2)(3h - 4)(h)
Now we have an equation with one variable, h, which we can solve to find the height of the triangle.
To find an expression for the base of the triangle:
Let's denote the height of the triangle as 'h'.
According to the given information, the base of the triangle is 4 less than 3 times the height.
Therefore, the expression for the base can be written as:
Base of the triangle = 3h - 4
To determine the equation for the area of the triangle:
The area of a triangle can be calculated using the formula A = (1/2) * base * height.
Given that the area of the triangle is 38 square cm, we can substitute the values into the formula to form an equation:
38 = (1/2) * [3h - 4] * h
The first step in solving for 'h' would be to simplify the equation by distributing the (1/2) to the terms inside the brackets:
38 = (3/2) * h^2 - 2h
We can then move all the terms to one side of the equation to set it equal to zero:
(3/2) * h^2 - 2h - 38 = 0
This is a quadratic equation, and to solve for 'h' we can proceed with factoring, completing the square, or using the quadratic formula.
To find the expression for the base of the triangle and the equation for the area of the triangle, let's first define some variables:
Let's denote:
- the height of the triangle as 'h' (in cm)
- the base of the triangle as 'b' (in cm)
Now, let's use the given information to derive the expression for the base of the triangle and the equation for the area of the triangle.
1. Expression for the base of the triangle (b):
According to the given information, the base of the triangle is 4 less than 3 times the height. We can express this mathematically as:
b = 3h - 4
So, the expression for the base of the triangle is (3h - 4).
2. Equation for the area of the triangle:
The formula for the area of a triangle is given by: A = (1/2) * base * height
Substituting the expression for the base (b) we derived earlier, we get:
A = (1/2) * (3h - 4) * h
Given that the area of the triangle is 38 square cm, we can set up the following equation:
38 = (1/2) * (3h - 4) * h
Now, let's move on to the first step in solving for h.
3. First step in solving for h:
To solve for h, we need to rearrange the equation and simplify it. Let's start by multiplying both sides of the equation by 2 to get rid of the fraction:
2 * 38 = (3h - 4) * h
Simplifying further:
76 = 3h^2 - 4h
This quadratic equation can be solved by rearranging it in standard form and factoring or using the quadratic formula.