SOLUTION: Ok so I'm given the diagonal of a square and I need to find the length of the sides. I know how to find diagonal but I don't know how to reverse it.

Question 508699: Ok so I'm given the diagonal of a square and I need to find the length of the sides. I know how to find diagonal but I don't know how to reverse it.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
First, we know that all sides of a square have the same dimension. Call this dimension X. We also know that all the corner angles of a square are 90 degrees. Therefore, when we draw a diagonal for the square we have created two right triangles. Each of the triangles has two legs. These two legs are the sides and we called each of them X. The diagonal is the hypotenuse of the right triangle. Let's call the length of the diagonal (hypotenuse) D
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The Pythagorean theorem tells us that in a right triangle, the sum of the squares of the two legs equals the square of the diagonal. For a square, both of the legs have the same dimension X, so the Pythagorean equation for a square is:
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The two terms on the left side can be added to give:
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Start solving for X by dividing both sides by 2 to get:
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Let's stop here. This tells you that if you are given the measurement of the diagonal (D) of a square you can solve for the sides by doing the following steps:
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(1) square the length of the diagonal
(2) divide 2 into the answer from step (1). This is the answer for the right side of the equation. It is
(3) the answer to step (2) is equal to . So to find X, just take the square root of the answer to step (2) and you have the length of the side of the given square.
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Don't let this all confuse you. For a square, if you are given the diagonal, just substitute it into the Pythagorean equation:
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(Remember for a square both the legs (sides) are equal, so X can be used for each leg.) Then just solve it. Example: suppose you are told that the diagonal (D) of a square is 10 units. Substitute that into the Pythagorean equation and you get:
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Square the right side:
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Add the two terms on the left side:
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Divide both sides by 2:
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Take the square root of both sides:
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The left side is just X and the right side shown below is equivalent to the square root of 50:
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The right side can be written as follows:
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And since 25 has 5 as its square root this reduces to the answer of:
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The right side is the length of the side of a square that has 10 units as its diagonal.
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Hope this helps you to understand how to work this problem.

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