Question

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: 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 \( h \).