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Problem 1: A square drawn below has an area of 144 cm2. What is the perimeter of the figure? Problem 2: There are 12 oranges, 16 apples and 24 lemons in a basket. Find the least number which can be di

Mathematics

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:
A square drawn below has an area of 144 cm2144 \text{ cm}^2. What is the perimeter of the figure?

  1. Find the side length of the square.

    The area of a square is given by the formula A=s2A = s^2, where ss is the side length.
    We are given A=144 cm2A = 144 \text{ cm}^2.

    s2=144 cm2s^2 = 144 \text{ cm}^2 s=144 cm2s = \sqrt{144 \text{ cm}^2} s=12 cms = 12 \text{ cm}
  2. Calculate the perimeter of the square.

    The perimeter of a square is given by the formula P=4sP = 4s.

    P=4×12 cmP = 4 \times 12 \text{ cm} P=48 cmP = 48 \text{ cm}

    The perimeter of the figure is 48 cm\boxed{\text{48 cm}}.

    :
    There are 12 oranges, 16 apples and 24 lemons in a basket. Find the least number which can be divided by the fruits.

    This question asks for the least common multiple (LCM) of the number of fruits.

  3. Find the prime factorization of each number.

    12=2×2×3=22×3112 = 2 \times 2 \times 3 = 2^2 \times 3^1 16=2×2×2×2=2416 = 2 \times 2 \times 2 \times 2 = 2^4 24=2×2×2×3=23×3124 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1
  4. Calculate the LCM.

    To find the LCM, take the highest power of each prime factor present in the numbers.
    The prime factors are 2 and 3.
    The highest power of 2 is 242^4 (from 16).
    The highest power of 3 is 313^1 (from 12 and 24).

    LCM(12,16,24)=24×31LCM(12, 16, 24) = 2^4 \times 3^1 LCM=16×3LCM = 16 \times 3 LCM=48LCM = 48

    The least number which can be divided by the fruits is 48\boxed{48}.

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