One side of a rectangle is 10 feet shorter than twice another side. find the length of the shorter side if we also know the perimeter of the rectangle is 28 feet.

  6 feet

Step-by-step explanation:

Let x represent the length of "another side." Then "one side" is ...

  2x -10 . . . . . . 10 feet shorter than twice another side

The sum of these two side lengths is half the perimeter, so is ...

  x + (2x -10) = 14 . . . . . two sides are half the perimeter

  3x = 24 . . . . . . . . . . . . add 10, collect terms

  x = 8 . . . . . . . . . . . . . . .divide by the coefficient of x

  (2x -10) = 2·8 -10 = 6 . . . . find "one side"

We have found "one side" to be 6 feet long, and "another side" to be 8 feet long. The shorter side is 6 feet.

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