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Math Help - Area of square

  1. #1
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    Area of square

    please tell me how to solve this problem

    The ratio of the area of square to that of the square drawn on its diagonal is:
    (A)1:3
    (B)3:4
    (C)2:3
    (D)1:2
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by rickymylv View Post
    please tell me how to solve this problem

    The ratio of the area of square to that of the square drawn on its diagonal is:
    (A)1:3
    (B)3:4
    (C)2:3
    (D)1:2


    Let x be the side of square (all sides equal)

    Length of its diagonal in terms of x = ?? ( Use Pythagoras theorem)
    -----------------------------------
    Area of square = (side)^2

    Now solve it !
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  3. #3
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    Given a square with sides of length s, the length of the diagonal of the square is equal to s\sqrt{2}

    The question asks for the ratio of the area of a square to the area of a square drawn on its diagonal. As in:

    \frac{s^2}{(s\sqrt{2})^2}
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  4. #4
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    Hello, rickymylv!

    Please tell me how to solve this problem

    The ratio of the area of a square to that of the square drawn on its diagonal is:

    . . (A)\;1:3 \qquad (B)\;3:4 \qquad (C)\;2:3 \qquad  (D)\;1:2
    A sketch is essential . . .
    Code:
          * - - - - - *
          |           |
          |           |
          |           | s
          |           |
          |           |
          * - - - - - *
                s
    A square with side s has area s^2.


    Code:
          * - - - - - *
          |   _     * |
          |  √2s  *   |
          |     *     | s
          |   *       |
          | *         |
          * - - - - - *
                s
    The diagonal d of the square can be found with Pythagorus:

    . . d^2 \:=\:s^2+s^2 \:=\:2s^2 \quad\Rightarrow\quad d \:=\:\sqrt{2}\,s

    The area of the square of side d is: . \left(\sqrt{2}\,s\right)^2 \;=\;2s^2



    Therefore, the ratio of the two areas is . . .

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  5. #5
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    hello

    let the side of the square be (a),so the area of the first square is a^2,
    then by pythegoras , it's diagonal is a√2,and the area of the second square ia (a√2)^2=2(a^2).
    therefore the ratio is:a^2 / 2(a^2)=1/2
    D is correct.
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