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
An expression for the base of the triangle:. Response area
Equation for the area of the triangle: Response area
The first step in solving for h:
Let's denote the height of the triangle as h.
According to the problem, the base of the triangle is 4 less than three times the height, so we can express the base as:
Base = 3h - 4
The equation for the area of a triangle is given as A = 1/2 * base * height. Since we have the area (A) as 38 square cm, we can substitute the values:
38 = 1/2 * (3h - 4) * h
The first step in solving for h would be to distribute the 1/2 to the terms in the brackets:
38 = 1/2 * 3h * h - 1/2 * 4 * h
Simplifying further,
38 = 3/2 * h^2 - 2h
Now, we need to solve this quadratic equation to find the value of h.
could you make it simplier
To find an expression for the base of the triangle, let's use the given information.
Let's assume the height of the triangle is h.
According to the given statement, the base of the triangle is 4 less than three times the height.
Therefore, we can write the expression for the base as:
Base = 3h - 4
To find the equation for the area of the triangle, we can use the formula for the area of a triangle:
Area = (base × height) / 2
Substituting the expression for the base we just found, the equation for the area of the triangle is:
Area = ((3h - 4) × h) / 2
Now, let's move on to solving for h.
To find an expression for the base of the triangle, we can use the given information that the base is 4 less than three times the height. Let's assume the height of the triangle is 'h'. So, the expression for the base would be:
Base = 3h - 4
Now, let's move on to the equation for the area of the triangle. The formula for the area of a triangle is given as:
Area = (base * height) / 2
In this case, the area of the triangle is given as 38 square cm. So, the equation for the area of the triangle would be:
38 = (Base * h) / 2
Next, let's solve for 'h' by rearranging the equation. Multiplying both sides by 2 to eliminate the fraction, we get:
76 = Base * h
Now, we have two equations:
1) Base = 3h - 4
2) 76 = Base * h
To solve for 'h', we can substitute the expression for the base (3h - 4) from the first equation into the second equation:
76 = (3h - 4) * h
Now, let's simplify this equation to solve for 'h'.