Missing length of a trapezoid

Question

Find the length of the shortest base of the trapezoid described: the height is 10 feet. One base is 4 feet longer than the other base. The area is 120 square feet. 

Answer 1

Answer: 10 feet

We know that the formula for the area of a trapezoid is A=((a+b)/2)(h)

If we make 'a' the long base and 'b' the short base, we can say that a=b+4, and b=b

Plug in the values we do know

120=((b+4+b)/2)(10) Combine the two 'b's'

120=((2b+4)/2)(10) Divide 2b+4 by 2

120=b+2(10) Distribute the 10

120=10b+20 Subtract 20

100=10b Divide by 10

b=10

Therefore the short base is 10 feet. This would make the long base (a), 14 feet if it is 4 more than the short base.