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

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

Answer 2

Option C is correct answer.

Explanation:

The area for the trapezoid is given as :

A=
`(B+b)*(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((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
`(a)/(6)-9`

Therefore, option C is the right answer.