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Rectangle Perimeter, Area and Ordered Diagonal Measurements

A feasible pair determines two side lengths up to exchange. This workflow chooses the larger as length and the smaller as width. Area cannot exceed half the squared diagonal; equality describes a square.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Longer or equal side l 4, Shorter or equal side w 3 gives Diagonal (d) 5, Area 12, Perimeter 14, Circumcircle radius 2.5, Diagonal angle opposite longer side 106.2602.

P = 2(l+w); A = lw; d² = l²+w²

Worked example

Enter these known values and leave the other values blank.

Longer or equal side l
4 cm
Shorter or equal side w
3 cm
Diagonal (d)
5 cm
Area
12 cm²
Diagonal angle opposite longer side
106.26 deg
Circumcircle radius
2.5 cm
Perimeter
14 cm

Assumptions and limitations

  • Length is the positive longer or equal side, and width is the shorter or equal side. The diagonal angle opposite length is right or obtuse; squares are included through the reviewed equality guards. Perimeter/area and area/diagonal inverses select larger length and smaller width. A real area/diagonal pair requires A no greater than d²/2. Perimeter alone cannot determine both sides.
  • Clear unknowns before solving backward and select compatible units. Original reference drawings do not scale to entered values. Independently rounded boundary measurements can be incompatible at finite precision.

Common questions

Does area and diagonal determine an ordered rectangle?

A feasible pair determines two side lengths up to exchange. This workflow chooses the larger as length and the smaller as width. Area cannot exceed half the squared diagonal; equality describes a square.

How many measurements are needed?

Use the worked example or a verified independent input pair or triple. Supplying dependent measurements does not add enough information; a consistent shape still needs a length scale.

Which input pairs support the retained inverse controls?

Use both sides; either side with area, perimeter or diagonal; the diagonal angle with a side, perimeter or diagonal; area with perimeter or diagonal; perimeter with diagonal; or circumcircle radius with one side. The larger root is length.

References

Require positive physical rectangle measures and real inverse roots, with equality allowed for square rectangles. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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