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

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 step by step, let's define the height of the triangle as \( h \) and the base \( b \).

1. An expression for the base of the triangle:
   The problem states that the base is four less than three times the height. This can be expressed as:
   \[ b = 3h - 4 \]

2. Equation for the area of the triangle, substituting in for the base:
   The area \( A \) of the triangle is given by the formula:
   \[ A = \frac{b \times h}{2} \] Substituting the expression for the base \( b \) into the area formula, we have:
   \[ 38 = \frac{(3h - 4) \times h}{2} \] To simplify this, we can multiply both sides by 2 to eliminate the fraction:
   \[ 76 = (3h - 4) \times h \]

3. The first step in solving for \( h \):
   The equation from the previous step can be rearranged:
   \[ 76 = 3h^2 - 4h \] Moving everything to one side to set the equation to zero gives:
   \[ 3h^2 - 4h - 76 = 0 \]
   This is a quadratic equation in standard form, which is the first step in solving for \( h \).

Now you can use the quadratic formula or factoring (if it's factorable) to solve for \( h \).

Answer 2

What is the Equation for the area of the triangle, substituting in for the base

Answer 3

The equation for the area of the triangle, substituting in for the base, is derived from the area formula:

\[ A = \frac{b \times h}{2} \]

Given that the base \( b \) is expressed as \( b = 3h - 4 \), we substitute this expression into the area formula:

\[ A = \frac{(3h - 4) \times h}{2} \]

Since the area of the triangle is given as 38 square centimeters, we can write:

\[ 38 = \frac{(3h - 4) \times h}{2} \]

To rearrange this to eliminate the fraction, we can multiply both sides by 2:

\[ 76 = (3h - 4) \times h \]

This is the equation for the area of the triangle, with the expression for the base substituted in.

Answer 4

there is no 76 = just 38 = (3h - 4 * h)/2

Answer 5

I apologize for any confusion. Let's clarify the equation explicitly with the correct substitution without additional steps.

Starting with the area formula:

\[ A = \frac{b \times h}{2} \]

We substitute \( b = 3h - 4 \) into the formula:

\[ A = \frac{(3h - 4) \times h}{2} \]

Since the area \( A \) is given as 38 square centimeters, we write:

\[ 38 = \frac{(3h - 4) \times h}{2} \]

This is the correct equation for the area of the triangle, substituting in for the base. Thank you for your patience!