Question

The function A(b) relates the area of a trapezoid with a given height of 10 and one base length of 7 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. 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

The function for the trapezoid area is:
A(x)=(B+b)*h/2
where B and b are the bases and h is the height.
With the given data: h=10 B and b =7 and x (it may vary which one is bigger)

So that function becomes:
A(x)=(7+x)*10/2
A(x)=(7+x)*5

So if you want the inverse function, you have to operate to find x:
A(x)/5=7+x
A(x)/5-7=x

So the new function is:
x(A)=A/5-7