Question

Which equation below represents the inverse function B(a) , which takes the trapezoid's area as input and returns as output the length of the other base?

Answer 1

Answer:

Option C is correct answer.

Step-by-step explanation:

The area for the trapezoid is given as :

A=$(B+b)*\frac{h}{2}$

where B and b are the bases and h is the height.  

The given height is : h=12 B and b =9

Function is :A(b) $12\frac{(b+9)}{2}$

This is simplified as A(b)=$6*(b+9)$

A(b)=$6b+54$

Subtracting 54 from both sides we get : A(b)-54=6b

Now divide both sides by 6 we get : Option C or $\frac{a}{6}-9$

Therefore, option C is the right answer.

Answer 2

A(b)  = 12(b + 9) / 2
12(b + 9) = 2 A(b)
b + 9 = 2 A(b) / 12  = A(b) / 6
b = A(b)
      ----- - 9
        6

B(a)   =  a              
             --  -  9
              6


It's C