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Math Help - Rectangle!

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    Junior Member whytechocolate01's Avatar
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    Post Rectangle!

    Find the area of a rectangle with length 4 and diagonal 5...

    I thought this was impossible because the diagonal must be longer than the length of a side so i'm not sure what to do. Please help!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by whytechocolate01 View Post
    Find the area of a rectangle with length 4 and diagonal 5...

    I thought this was impossible because the diagonal must be longer than the length of a side so i'm not sure what to do. Please help!
    did you draw a diagram. always draw a diagram if possible--especially for a geometry question. if we consider just a half of the rectangle, that is, the portion on either side of the diagonal, we realize that it forms a right-angled triangle with a hypotenuse of 5 and a base of 4 (draw a diagram to see this). just find the area of that triangle and multiply it by two. if you are still having problems, get back to me.
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    Quote Originally Posted by whytechocolate01 View Post
    Find the area of a rectangle with length 4 and diagonal 5...

    I thought this was impossible because the diagonal must be longer than the length of a side so i'm not sure what to do. Please help!
    Hello,

    1. The area of a rectangle can be calculated by: A = length * width.
    You know already: l = 4

    2. The diagonal d divides the rectangle into 2 right triangles. The diagonal is the hypotenuse of the triangle. Use Pythagorean theorem to calculate the missing side w:

    d = l + w ==> w = d - l ==> w = √(d - l)

    Therefore w = √(5 - 4) = √(25 - 16) = √(9) = 3

    3. Plug in the values into the formula: A = 4 * 3 = 12 square units
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