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Convert the mixed number to an improper fraction.

Mathematics

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Answer

174\frac{\sqrt{17}}{4}

1

32 cm32 \text{ cm}

Step-by-step solution

5 steps

  1. Convert the mixed number to an improper fraction.

    1116=1×16+116=17161\frac{1}{16} = \frac{1 \times 16 + 1}{16} = \frac{17}{16}

  2. Find the square root of the improper fraction.

    1716=1716\sqrt{\frac{17}{16}} = \frac{\sqrt{17}}{\sqrt{16}} 174\frac{\sqrt{17}}{4}

    The value is 174\boxed{\frac{\sqrt{17}}{4}}.

  3. Perform the division.

    When a number is divided by itself, the result is 1, provided the number is not zero.

    3729÷3729=1\frac{3}{729} \div \frac{3}{729} = 1

    Alternatively, invert the second fraction and multiply:

    3729×7293=3×729729×3=1\frac{3}{729} \times \frac{729}{3} = \frac{3 \times 729}{729 \times 3} = 1

    The simplified expression is 1\boxed{1}.

  4. Recall the properties of a kite.

    A kite is a quadrilateral with two distinct pairs of equal-length adjacent sides. This means that if the sides are 7 cm and 9 cm, there are two sides of length 7 cm and two sides of length 9 cm.

  5. Calculate the perimeter.

    The perimeter is the sum of the lengths of all sides.

    Perimeter=7 cm+7 cm+9 cm+9 cm\text{Perimeter} = 7 \text{ cm} + 7 \text{ cm} + 9 \text{ cm} + 9 \text{ cm} Perimeter=2(7 cm)+2(9 cm)\text{Perimeter} = 2(7 \text{ cm}) + 2(9 \text{ cm}) Perimeter=14 cm+18 cm\text{Perimeter} = 14 \text{ cm} + 18 \text{ cm} Perimeter=32 cm\text{Perimeter} = 32 \text{ cm}

    The perimeter of the kite is 32 cm\boxed{32 \text{ cm}}.

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