Rearrange formulas to isolate a chosen quantity and interpret the result.
Decide whether two algebraic forms are equivalent rearrangements of a formula
Problem
Decide whether \(l~=~(P~-~2w)/2\) and \(l~=~P/2~-~w\) are equivalent rearrangements of \(P~=~2l~+~2w\).
Big Picture
What this problem is really about
Equivalence should be tested by transforming one form into the other, not by judging how different they look. We’ll start with the grouped quotient, apply its common divisor to every term in the numerator, and simplify. Reversing the rearrangement into the original perimeter formula provides a second check that the two expressions describe the same quantity.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
