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Homework Help: Rectangle geometry problem

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    A rectangle is 2 metres longer than it is wide. On the other hand, if each side of the rectangle is increased by 2 metres, then the area increases by 24 square metres. Find the side-lengths of the rectangle.

    2. Relevant equations

    3. The attempt at a solution
    So my thoughts on dealing with this problem are to let the width = x , then the length = x + 2

    The area of a rectangle is length multiplied by width, so I figured [itex] x(x+2) + 24 = 2x + 2(x+2)[/itex]

    I thought that this would make sense but it doesn't really when I try to solve for x.
  2. jcsd
  3. Oct 29, 2012 #2


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    width=x, length=x+2, area would be x(x+2)

    On the other hand, if each dimension is increased by 2, then:
    width = (x)+2, and length = (x+2)+2, and area would be (x+2)((x+2)+2)
    or, taking care of calculation through grouping symbols,
    width = x+2 and length = x+4, and area would be (x+2)(x+4)

    Notice that part of the problem description specified a difference in area between the original rectangle and the augmented rectangle, of 24 square meters.
  4. Oct 29, 2012 #3
    Thank you.
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