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Find missing side lengths from perimeter

Perimeter is the total distance around a polygon, so a missing side length can be determined by subtracting the sum of the known side lengths from the given perimeter and expressing the relationship with an equation. The reasoning applies to diagrams with whole-number, decimal, or simple fractional measurements, including rectangles where opposite sides are equal; it distinguishes perimeter from area and supports solving one-step equations.

Detailed Explanation: Find missing side lengths from perimeter

Perimeter is the total distance around a shape. To find a missing side:

  1. Add the known side lengths.
  2. Subtract that sum from the perimeter.
  3. Check that all side lengths add to the given perimeter.

Example: A polygon has a perimeter of (32)(32) cm. Four sides measure 66 cm, 88 cm, 55 cm, and 77 cm. The fifth side is xx cm. Find xx.

Write an equation using the perimeter:

6+8+5+7+x=326+8+5+7+x=32

First, add the known side lengths:

6+8+5+7=266+8+5+7=26

Now subtract (26)(26) from the total perimeter:

x=32−26x=32-26 x=6 cmx=6\text{ cm}

So, the missing side length is 66 cm.

Check:

6+8+5+7+6=32 cm6+8+5+7+6=32\text{ cm}

The total is (32)(32) cm, so the answer is correct. Remember, perimeter measures the distance around a shape, not the space inside it.

Learn by doing: Find missing side lengths from perimeter

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    Perimeter of a Rectangle - Side from Perimeter and Side

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