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Math Help - Rectangle problem-probably easy

  1. #1
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    Rectangle problem-probably easy

    Suppose the length of a rectangle is twice the width. If we increase both the width and length of the rectangle by 2 units, the area is increased by 34 square units. Find the width of the rectangle.

    Can someone explain the process of finding the answer?
    Here are the answer choices:

    a)3
    b)8
    c)10
    d)5
    e)none of these
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  2. #2
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    Hello, alaricepent!

    Make a sketch, then baby-talk your way through it . . .


    Suppose the length of a rectangle is twice the width.
    If we increase both the width and length of the rectangle by 2 units,
    the area is increased by 34 square units.
    Find the width of the rectangle.

    . . (a)\;3 \qquad (b)\;8 \qquad (c)\;10 \qquad (d)\;5 \qquad(e)\text{ none of these}
    Code:
                2x
          *-------------*
          |             |
        x |             | x
          |             |
          *-------------*
                2x
    Let x = width
    Then 2x = length.
    . . The area is: . A_1 \:=\:(2x)(x) \:=\:2x^2


    Code:
                 2x+2
          *-------------*---*
          |             :   |
          |             :   |
     x+2  |             :   | x+2
          * - - - - - - *   |
          |                 |
          *-----------------*
                 2x+2
    Now x+2 = width
    and 2x+2 = length
    . . The area is: . A_2 \;=\;(x+2)(2x+2) \:=\:2x^2+6x+4


    The new area is 34 more than the original area:
    . . 2x^2 + 6x + 4 \;=\;2x^2 + 34

    So we have: . 6x \:=\:30 \quad\Rightarrow\quad x \:=\:5


    The width is 5 . . . answer (d)

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