Solve A = (a + b)h/2 for h

Step by step

The question

Question: solve for h in A = (a + b)h/2.

We treat the other letters like numbers.

1 h on the left

h is on the right.

We swap the two sides, so h is on the left.

They are still equal.

2 Remove the fraction

There is a fraction: over 2.

Times 2 removes it.

We do it on both sides.

2/2 is 1.

The fraction is gone.

Now we have (a + b)h = 2A.

3 Remove the (a + b)

(a + b)h means (a + b) times h.

We want just h.

To remove times (a + b), we divide by (a + b).

We do it on both sides.

(a + b) divided by (a + b) is 1.

So just h is left.

So h = 2A/(a + b).

4 Check

Let's check with numbers.

We pick A = 3, a = 2, b = 4.

Our answer gives h = 1.

Now we put all the numbers into the start.

First the left side.

Now the right side.

Both sides are 3.

So our answer is right!

Let's look back.

First: h on the left.

Then: remove the fraction.

Then: remove the (a + b).

Last: check.