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Grade 8 learners were asuad by their teacher to Construct a square whose length is 40mm using a Compass and a ruler only. Construct a square as reqired by the teacher. Measure and dimension theor diagonal of the square.

Mathematics

ScanSolve AI Answer

Answer

56.57 mm56.57 \text{ mm}

Step-by-step solution

5 steps

  1. Identify the given information.

    The side length of the square (ss) is 40 mm40 \text{ mm}.

  2. Recall the formula for the diagonal of a square.

    For a square with side length ss, the diagonal dd can be found using the Pythagorean theorem:

    d2=s2+s2d^2 = s^2 + s^2 d2=2s2d^2 = 2s^2 d=2s2d = \sqrt{2s^2} d=s2d = s\sqrt{2}

  3. Substitute the given side length into the formula.

    d=40 mm×2d = 40 \text{ mm} \times \sqrt{2}

  4. Calculate the value of the diagonal.

    d≈40×1.41421356d \approx 40 \times 1.41421356 d≈56.56854249 mmd \approx 56.56854249 \text{ mm}

  5. Round the answer to a suitable number of decimal places (e.g., two decimal places).

    d≈56.57 mmd \approx 56.57 \text{ mm}

    The diagonal of the square is 56.57 mm56.57 \text{ mm}.

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