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Math Help - Solving for side of square given diagonal

  1. #1
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    Solving for side of square given diagonal

    Can someone correct me?

    Problem: The diagonal of a square quilt is 4 times the square root of 2. What is the area of the quilt in square feet?

    The answer is 4. My book suggests that we use the property of a 45 45 90 triangle to solve this. I understand that method. However, I initially attempted to solve it by using Pythagorean theorem with the diagonal being the hypotenuse. I came up with 4 x 2^(1/2) = 2 x (a^2) I proceeded to divide the left side by 2, and I did not come up with 4 for the answer. Why is this?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Solving for side of square given diagonal

    If you want to use Phytagoras then, let a be the side of the square quilt therefore:
    a^2+a^2=(4\sqrt{2})^2
    Solve this equation for a.
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  3. #3
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    Re: Solving for side of square given diagonal

    Quote Originally Posted by benny92000 View Post
    Can someone correct me?

    Problem: The diagonal of a square quilt is 4 times the square root of 2. What is the area of the quilt in square feet?

    The answer is 4. <--- That is the side-length and not the area
    My book suggests that we use the property of a 45 45 90 triangle to solve this. I understand that method. However, I initially attempted to solve it by using Pythagorean theorem with the diagonal being the hypotenuse. I came up with 4 x 2^(1/2) = 2 x (a^2) I proceeded to divide the left side by 2, and I did not come up with 4 for the answer. Why is this?
    1. Draw a sketch.

    2. The quilt is placed inside a square of the side-length d.

    3. You can prove (by congruent triangles) that the area of the quilt is

    A = \frac12 \cdot d^2

    4. Plug in the value for d and you'll get the given result.

    5. If you want to calculate the side-length then a = \sqrt{A}=d \cdot \sqrt{\frac12}
    Attached Thumbnails Attached Thumbnails Solving for side of square given diagonal-quadflaeche_diag.png  
    Last edited by earboth; August 16th 2011 at 11:54 PM.
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  4. #4
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    Re: Solving for side of square given diagonal

    Siron has calculated the sides of the square when what was asked for was the area, s^2.
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  5. #5
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    Re: Solving for side of square given diagonal

    Quote Originally Posted by cathectio View Post
    Siron has calculated the sides of the square when what was asked for was the area, s^2.
    no kidding ...

    Siron most probably assumed the OP was capable of determining the area of a square once he/she determined the side length.

    Effective tutoring sometimes requires providing just enough information to let the OP solve the problem (or screw it up) on their own.
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