Answered

The length of a rectangle is 10 feet longer than it is wide. If each side is increased 10 feet, then the area is multiplied by 2. What was the size of the original rectangle?

The width or short side is _____ feet
The length or long side is _____ feet



Answer :

sqdancefan

Answer:

  • width: 20 ft
  • length: 30 ft

Step-by-step explanation:

You want the length and width of a rectangle that is 10 ft longer than wide if adding 10 ft to each dimension doubles its area.

Area

The original area will be the product of the length and width:

  A = LW = (W+10)W

The area with increased dimensions is ...

  A = (L+10)(W+10)

We want the increased area to be twice the original area:

  2(W+10)(W) = ((W+10)+10)(W+10) . . . . . . use W+10 for L

  2W = W +20 . . . . . . . . divide both sides by W+10

  W = 20 . . . . . . . . . . subtract W

Dimensions

The original width is 20 ft. The original length is 30 ft.

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Additional comment

If we were to write the equation for area in standard form, it would be a quadratic in W. One of its factors would be (W+10). We can divide that out because we know that W=-10 is not a solution.

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