The equation below shows the area of a trapezoid, [tex]\( A \)[/tex], with a height of [tex]\( 9 \text{ cm} \)[/tex] and one base [tex]\( 35 \text{ cm} \)[/tex].

[tex]\[ A = \frac{9}{2}(b + 35) \][/tex]

Which of the following formulas correctly solves for the other base, [tex]\( b \)[/tex]?

A. [tex]\( b = \frac{2A}{9} + 35 \)[/tex]

B. [tex]\( b = \frac{2A}{9} - 35 \)[/tex]

C. [tex]\( b = \frac{2A + 35}{9} \)[/tex]

D. [tex]\( b = \frac{2A - 35}{9} \)[/tex]



Answer :

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]