The base of a triangle is four less than three times the height. The area of the triangle is 38 square centimeters. A = (b x h)/2

Question

An expression for the base of the triangle: ______________
Equation for the area of the triangle, substituting in for the base: _____________
The first step in solving for h: ______________
Fill In The Blanks
Options: Divide both sides by h, 4h - 3, Multiply both sides by 2, 4 - 3h, 3h - 4, 3h - 4 = 1/2(38 x h), 38 = (3h - 4 x h)/2

Answer 1

Let's fill in the blanks step by step.

1. An expression for the base of the triangle:
   The base \( b \) is four less than three times the height \( h \). This can be expressed as:
   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 \( b \) with \( 3h - 4 \):
   A = (3h - 4) \cdot h / 2
   Since the area is given as 38 square centimeters, we write:
   38 = (3h - 4) \cdot h / 2

3. The first step in solving for h:
   To eliminate the fraction, the first step is to multiply both sides by 2:
   Multiply both sides by 2

Combining them together, here are the finished responses:

1. Expression for the base: 3h - 4
2. Equation for the area: 38 = (3h - 4) \cdot h / 2
3. First step in solving for h: Multiply both sides by 2