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EFGHEFGH is a rhombus. Given EG=16EG=16 and FH=12FH=12, what is the length of one side of the rhombus?\newline66 units\newline88 units\newline1010 units\newline1414 units

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Q. EFGHEFGH is a rhombus. Given EG=16EG=16 and FH=12FH=12, what is the length of one side of the rhombus?\newline66 units\newline88 units\newline1010 units\newline1414 units
  1. Form Right-Angled Triangles: A rhombus has diagonals that bisect each other at right angles. To find the length of one side of the rhombus, we can use the diagonals to form right-angled triangles. Each triangle will have half the length of each diagonal as its legs.\newlineCalculation: Half of EG=162=8EG = \frac{16}{2} = 8 units, Half of FH=122=6FH = \frac{12}{2} = 6 units
  2. Use Pythagorean Theorem: Using the Pythagorean theorem for one of the right-angled triangles formed by the diagonals, we can find the length of one side of the rhombus (which is the hypotenuse of the triangle). The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse cc is equal to the sum of the squares of the other two sides aa and bb.
    Calculation: c2=a2+b2c^2 = a^2 + b^2, where cc is the length of one side of the rhombus, aa is half of EG, and bb is half of FH.
  3. Substitute Values: Substitute the values of aa and bb into the Pythagorean theorem to find c2c^2.\newlineCalculation: c2=82+62=64+36=100c^2 = 8^2 + 6^2 = 64 + 36 = 100
  4. Find Length of Side: Find the value of cc by taking the square root of c2c^2.\newlineCalculation: c=100=10c = \sqrt{100} = 10 units

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