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)

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)

Options for the "response areas", 3h - 4 = 1/2 (38 x h), 3h - 4, 4 - 3h, 38 = (3h-4xh)/2, Divide both sides by h, Multiply both sides by 2, 4h - 3

Answer 1

Let's break down the problem step by step.

1. An expression for the base of the triangle:

   The problem states that the base is four less than three times the height. If we let \( h \) represent the height, then the base \( b \) can be expressed as: \[ b = 3h - 4 \]

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 \( A = \frac{b \times h}{2} \). Given that the area is 38 square centimeters, we substitute for \( b \): \[ 38 = \frac{(3h - 4) \times h}{2} \]

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

   To eliminate the fraction, we can multiply both sides of the equation by 2: \[ 76 = (3h - 4) \times h \]

Now we can review the response areas based on our findings:

• An expression for the base of the triangle: \( 3h - 4 \)

• Equation for the area of the triangle, substituting in for the base: \( 38 = (3h - 4) \times h / 2 \) (but after multiplying by 2, it becomes \( 76 = (3h - 4) \times h \))

• The first step in solving for \( h \): Multiply both sides by 2 (leading to \( 76 = (3h - 4)h \))

So, if you need to fill in the response areas, here is how you would do it:

1. Response: \( 3h - 4 \)
2. Response: \( 38 = (3h - 4) \times h / 2 \) or \( 76 = (3h - 4) \times h \) (after multiplying by 2)
3. Response: Multiply both sides by 2