Finding the Length of a Rectangle Given Its Perimeter and Width
Apply the geometry problem-solving strategy using the rectangle perimeter formula when the perimeter and one dimension are known, requiring a two-step equation to find the missing dimension.
Problem: Find the length of a rectangle with perimeter inches and width inches.
- Read: A rectangle has in. and in.; find the length. Draw and label the figure.
- Identify: The length of the rectangle.
- Name: Let = the length.
- Translate: Write the perimeter formula and substitute the known values:
- Solve: Multiply: . Subtract from both sides: . Divide both sides by : , which gives .
- Check: Add all four sides: , and checkmark
- Answer: The length is inches.
Unlike computing the perimeter from two known sides — which involves only multiplication and addition — this problem requires solving a two-step linear equation: first subtracting the width-related term () from the perimeter, then dividing by to isolate the length. This demonstrates how the perimeter formula can be used in reverse to find a missing dimension when the perimeter and one side length are known.
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