What is the step by step method for solving A=1/2bh(a+b) by making b the subject formula.
To make b the subject of the formula A = 1/2bh(a + b), follow these steps:
Step 1: Expand the bracket by multiplying the terms within it:
A = 1/2bh(a) + 1/2bh(b)
Step 2: Distribute (a) to the terms within the bracket:
A = 1/2bha + 1/2bhb
Step 3: Combine like terms:
A = 1/2bha + 1/2b^2h
Step 4: Rearrange the equation by isolating the term containing 'b':
A - 1/2b^2h = 1/2bha
Step 5: Move the 1/2bha term to the other side of the equation:
A - 1/2b^2h - 1/2bha = 0
Step 6: Factor out 'b' from the terms on the left side:
- 1/2bha - 1/2b^2h = b(A - 1/2ah - 1/2bh)
Step 7: Divide through by the factor on the right side, (A - 1/2ah - 1/2bh):
(- 1/2bha - 1/2b^2h) / (A - 1/2ah - 1/2bh) = b
Therefore, the formula for making b the subject is:
b = (- 1/2bha - 1/2b^2h) / (A - 1/2ah - 1/2bh)