The height of a trapezoid is 8 inches and it's area is 96 inches. One base of the trapezoids is 6 inches longer than the other base. What are the lengths of the bases? Explain how you found your answer

There is a common equation we use to find the Area of a trapezoid.

(a+b) h/2=A

Let's fill in what we know. We're not going to fill in any information about the bases.

(a+b) 8/2=96

We can already tell that 8/2 will simplify to 4.

(a+b) 4=96

Let's divide each side by 4.

a+b=24

Now, let's look at the information about the bases.

So, we will have this in terms of base a, since one base is longer than the other. This is how it'll look.

a + (a+6) = 24

We can simplify that further.

2a+6=24

now subtract 6 from each side.

2a=18

Let's divide

9=a

So one side is 9, so the other one is 15. We should make sure everything makes sense by putting all the information in the formula to find area.

(9+15) 8/2

24*4

96.

The lengths of the bases are 9 and 15 inches.