19. 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
(3 points)
An expression for the base of the triangle: _______
Equation for the area of the triangle, substituting in for the base: _______
The first step in solving for h: ______
Let the height of the triangle be h.
1) An expression for the base of the triangle:
The base of the triangle is four less than three times the height.
So, the expression for the base is:
(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.
Given that the area of the triangle is 38 square centimeters, we can substitute the expression for the base and the height into the equation:
38 = (1/2) * ((3h) - 4) * h
3) The first step in solving for h:
The given equation is quadratic in nature, so we can rewrite it in standard form:
0 = (1/2) * 3h^2 - 2h - 38
Now, the first step in solving for h is to multiply the entire equation by 2 to eliminate the fraction:
0 = 3h^2 - 4h - 76
To find the expression for the base of the triangle, let's assume the height of the triangle as 'h'. The given information states that the base is four less than three times the height.
Expression for the base of the triangle: 3h - 4.
The formula for the area of a triangle is given by A = (1/2)bh, substituting in the expression for the base of the triangle:
Equation for the area of the triangle: 38 = (1/2)(3h - 4)(h)
The first step in solving for h would be to simplify the equation:
1) Distribute (1/2) to (3h - 4) and multiply it with 'h'.
38 = (3/2)h^2 - 2h
Now, we have a quadratic equation.