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Math Help - Photo Dimensions

  1. #1
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    Photo Dimensions

    A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
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  2. #2
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    Hello, magentarita!

    Did you make a sketch?


    A photo is 3 inches longer that it is wide.
    A 2-inch border is placed around the photo.
    The total area of the photo and border is 108 square inches.
    What are the dimensions of the photo?
    Code:
            : 2 :  - W+3 -  : 2 :
          - *---*-----------*---*  -
          2 |   :           :   |  :
          - * - *-----------* - *  :
          : |   |           |   |  :
          W |   |W          |   | W+4
          : |   |    W+3    |   |  :
          - * - *-----------* - *  :
          2 |   :           :   |  :
          - *---*-----------*---*  -
            : - - -  W+7  - - - :

    Let W = width of the photo.
    Then W + 3 = length of the photo.

    With a two-inch border, the object has length W + 7 and width W+4

    The total area is 108: . (W+7)(W+4) \:=\:108 \quad\Rightarrow\quad W^2 + 11W - 80 \:=\:0

    . . which factors: . (W - 5)(W + 16) \:=\:0

    . . and has the positive root: . W \,=\,5


    Therefore, the dimensons of the photo are: .  5 \times 8 inches.

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  3. #3
    MHF Contributor
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    amazing.........

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!

    Did you make a sketch?

    Code:
            : 2 :  - W+3 -  : 2 :
          - *---*-----------*---*  -
          2 |   :           :   |  :
          - * - *-----------* - *  :
          : |   |           |   |  :
          W |   |W          |   | W+4
          : |   |    W+3    |   |  :
          - * - *-----------* - *  :
          2 |   :           :   |  :
          - *---*-----------*---*  -
            : - - -  W+7  - - - :
    Let W = width of the photo.
    Then W + 3 = length of the photo.

    With a two-inch border, the object has length W + 7 and width W+4

    The total area is 108: . (W+7)(W+4) \:=\:108 \quad\Rightarrow\quad W^2 + 11W - 80 \:=\:0

    . . which factors: . (W - 5)(W + 16) \:=\:0

    . . and has the positive root: . W \,=\,5


    Therefore, the dimensons of the photo are: .  5 \times 8 inches.
    Soroban, you are amazing in terms of math. Through your help, I will be ready for calculus next semester. Are you willing to help me? I have to take calculus 1-3, differential equations and linear algebra in future semesters.

    Thanks again.
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