Rectangle from Area and Perimeter
Recover a rectangle’s two side lengths from its area and perimeter. Detect impossible measurements and the square boundary, with a dimensioned outline.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Half the perimeter is the sum of the two sides and area is their product. Solve the resulting quadratic. A negative discriminant means no real rectangle can have those measurements.
x+y=P/2; xy=A; x,y=[P/2±√((P/2)²−4A)]/2
Worked example
Area24m² and perimeter20m give sides4m and6m. Area25m² with the same perimeter gives a5m square; any larger area is impossible.
Assumptions and input details
Fractions and decimals up to six places are accepted, with input magnitude at most1e6 and reduced denominator at most1e6. Exact fractions determine the result; decimal displays and diagrams are rounded. Area uses the square of the selected coordinate unit; perimeter uses that unit directly. Positive area and perimeter are required. Side lengths and diagrams are approximate.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Feasibility uses exact fractions. Recovered side lengths and the diagram use floating-point square roots.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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