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

Question

(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
An expression 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

Answer 1

To solve the problem with the given conditions, let's break it down step by step.

1. An expression for the base of the triangle:
   Let's denote the height of the triangle as \( h \). According to the problem, the base \( b \) is four less than three times the height. Thus, the expression for the base is:
   Response: b = 3h - 4

2. Equation for the area of the triangle, substituting in for the base:
   The formula for the area \( A \) of a triangle is given by:
   \[ A = \frac{1}{2} \times b \times h \]
   Since we know the area is 38 square centimeters, we can substitute our expression for the base:
   \[ 38 = \frac{1}{2} \times (3h - 4) \times h \]
   Rearranging gives us:
   Response: 38 = (1/2)(3h - 4)(h)

3. The first step in solving for \( h \):
   To eliminate the fraction, we can multiply both sides of the equation by 2:
   \[ 76 = (3h - 4) \times h \]
   This step breaks it down to a simpler quadratic equation:
   Response: Multiply both sides by 2.

These responses summarize the expressions and steps needed to set up and begin solving for the height of the triangle.