To determine which formula correctly solves for the base [tex]\( b \)[/tex] in the given trapezoid area equation, we can follow a step-by-step algebraic process.
The given area equation for the trapezoid is:
[tex]\[ A = \frac{9}{2}(b + 35) \][/tex]
Our goal is to solve for [tex]\( b \)[/tex].
### Step 1: Isolate the term containing [tex]\( b \)[/tex]
First, we want to isolate the term [tex]\( b + 35 \)[/tex]. To do this, we can multiply both sides of the equation by [tex]\(\frac{2}{9}\)[/tex]:
[tex]\[ \frac{2}{9} \cdot A = \frac{2}{9} \cdot \frac{9}{2}(b + 35) \][/tex]
The right side simplifies as follows:
[tex]\[ \frac{2}{9} \cdot \frac{9}{2} = 1 \][/tex]
So, we have:
[tex]\[ \frac{2A}{9} = b + 35 \][/tex]
### Step 2: Solve for [tex]\( b \)[/tex]
Next, we need to isolate [tex]\( b \)[/tex]. We can do this by subtracting [tex]\( 35 \)[/tex] from both sides:
[tex]\[ b = \frac{2A}{9} - 35 \][/tex]
Therefore, the correct formula to solve for the base [tex]\( b \)[/tex] is:
[tex]\[ b = \frac{2A}{9} - 35 \][/tex]
So, the correct answer is:
[tex]\[ b=\frac{2 A}{9}-35 \][/tex]
