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)

Question

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:

Answer 1

Let's break down the problem step by step.

1. Expression for the base of the triangle:

   If we let \( h \) represent the height of the triangle, then according to the problem, the base \( b \) is defined as: \[ b = 3h - 4 \]

2. Equation for the area of the triangle, substituting in for the base:

   The area \( A \) of a triangle is given by the formula: \[ A = \frac{b \times h}{2} \] Substituting in the expression for the base \( b \): \[ 38 = \frac{(3h - 4) \times h}{2} \]

3. The first step in solving for \( h \):

   To eliminate the fraction, you can multiply both sides of the equation by 2: \[ 76 = (3h - 4) \times h \] This is the first step toward solving for \( h \).

After this step, you can proceed to solve the equation \( 76 = 3h^2 - 4h \) for \( h \).