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B. In square EFGH, find the length of EG.

B. In square EFGH, find the length of EG.-example-1
User Luissquall
by
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1 Answer

1 vote

Answer:

6√2

Explanation:

You want one side of a square whose half-diagonal has length 6.

Right triangle

If X is the center point of the square where the diagonals cross at right angles, triangle EXG is an isosceles right triangle with leg length 6. The hypotenuse of an isosceles right triangle is √2 times the leg length, so ...

EG = 6√2

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Additional comment

If you like, you can use the Pythagorean theorem to prove that.

EG² + EX² +GX² = 6² +6² = 72

EG = √72 = √(36·2) = 6√2

A square is a rhombus, so the diagonals cross at right angles. A square is a rectangle, so the diagonals are the same length. A square is a parallelogram, so the diagonals bisect each other.