Formulas & advanced ratio expressions:
Solving for w: S-2lw =h
---------
2w+2l
To solve for the variable "w" in the equation S-2lw = h / (2w+2l), we can follow these steps:
Step 1: Distribute the division
Multiply both sides of the equation by 2w+2l to eliminate the denominator:
(S-2lw) * (2w+2l) = h
Step 2: Expand and simplify
Apply the distributive property to both terms in the left side of the equation:
2w(S) + 2l(S) - 2lw(2w) - 2lw(2l) = h
Multiply each pair of terms and arrange them in a simplified form:
2wS + 2lS - 4lw² - 4l²w = h
Step 3: Collect like terms
Rearrange the equation by combining the terms with w and the constants on one side:
2wS - 4lw² - 4l²w = h - 2lS
Step 4: Group the terms with w
Factor out w from the terms with w:
w(2S - 4lw - 4l²) = h - 2lS
Step 5: Solve for w
Divide both sides of the equation by (2S - 4lw - 4l²):
w = (h - 2lS) / (2S - 4lw - 4l²)
There you have it! The formula to solve for w in the expression S-2lw = h / (2w+2l) is w = (h - 2lS) / (2S - 4lw - 4l²).