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Rectangle A has side lengths of 6cm and 3.5cm. The side lengths of rectangle B are proportional to the side lengths of rectangle A. What could be the side lengths of rectangle B ? Choose 2 answers: (A) 3cm and 1.75cm (B) 5cm and 2.5cm (C) 7cm and 7cm (D) 12cm and 5cm (E) 5.25cm and 9cm

Rectangle A A has side lengths of 6 cm 6 \mathrm{~cm} and 3.5 cm 3.5 \mathrm{~cm} . The side lengths of rectangle B B are proportional to the side lengths of rectangle A A .\newlineWhat could be the side lengths of rectangle B B ?\newlineChoose 22 answers:\newline(A) 3 cm 3 \mathrm{~cm} and 1.75 cm 1.75 \mathrm{~cm} \newline(B) 5 cm 5 \mathrm{~cm} and 2.5 cm 2.5 \mathrm{~cm} \newline(C) 7 cm 7 \mathrm{~cm} and 7 cm 7 \mathrm{~cm} \newline(D) 12 cm 12 \mathrm{~cm} and 5 cm 5 \mathrm{~cm} \newline(E) 5.25 cm 5.25 \mathrm{~cm} and 9 cm 9 \mathrm{~cm}

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Q. Rectangle A A has side lengths of 6 cm 6 \mathrm{~cm} and 3.5 cm 3.5 \mathrm{~cm} . The side lengths of rectangle B B are proportional to the side lengths of rectangle A A .\newlineWhat could be the side lengths of rectangle B B ?\newlineChoose 22 answers:\newline(A) 3 cm 3 \mathrm{~cm} and 1.75 cm 1.75 \mathrm{~cm} \newline(B) 5 cm 5 \mathrm{~cm} and 2.5 cm 2.5 \mathrm{~cm} \newline(C) 7 cm 7 \mathrm{~cm} and 7 cm 7 \mathrm{~cm} \newline(D) 12 cm 12 \mathrm{~cm} and 5 cm 5 \mathrm{~cm} \newline(E) 5.25 cm 5.25 \mathrm{~cm} and 9 cm 9 \mathrm{~cm}
  1. Understand Proportionality: Understand the concept of proportionality.\newlineIf the side lengths of rectangle BB are proportional to the side lengths of rectangle AA, it means that the ratio of the corresponding sides of rectangle BB to rectangle AA must be the same.
  2. Calculate Ratio of Rectangle A: Calculate the ratio of the side lengths of rectangle A. The side lengths of rectangle A are 6 cm6\,\text{cm} and 3.5 cm3.5\,\text{cm}. To find the ratio, we divide one side by the other. Ratio = 6 cm3.5 cm=127\frac{6\,\text{cm}}{3.5\,\text{cm}} = \frac{12}{7}
  3. Check Pair A: Check each pair of side lengths for rectangle B to see if they maintain the same ratio of 127\frac{12}{7}.
    A. For the side lengths 3 cm3\,\text{cm} and 1.75 cm1.75\,\text{cm}:
    Ratio = 3 cm1.75 cm=63.5=127\frac{3\,\text{cm}}{1.75\,\text{cm}} = \frac{6}{3.5} = \frac{12}{7}
    This pair maintains the same ratio, so it is a possible solution.
  4. Check Pair B: Check the next pair of side lengths.\newlineB. For the side lengths 5 cm5\,\text{cm} and 2.5 cm2.5\,\text{cm}:\newlineRatio = 5 cm2.5 cm=105=21\frac{5\,\text{cm}}{2.5\,\text{cm}} = \frac{10}{5} = \frac{2}{1}\newlineThis ratio is not equal to 127\frac{12}{7}, so this pair is not a possible solution.
  5. Continue Checking: Continue checking the remaining pairs.\newlineC. For the side lengths 7 cm7\,\text{cm} and 7 cm7\,\text{cm}:\newlineRatio = 7 cm7 cm=11\frac{7\,\text{cm}}{7\,\text{cm}} = \frac{1}{1}\newlineThis ratio is not equal to 127\frac{12}{7}, so this pair is not a possible solution.
  6. Check Pair C: Check the next pair of side lengths.\newlineD. For the side lengths 12 cm12\,\text{cm} and 5 cm5\,\text{cm}:\newlineRatio = 12 cm5 cm=125\frac{12\,\text{cm}}{5\,\text{cm}} = \frac{12}{5}\newlineThis ratio is not equal to 127\frac{12}{7}, so this pair is not a possible solution.
  7. Check Pair D: Check the last pair of side lengths.\newlineE. For the side lengths 5.25 cm5.25\,\text{cm} and 9 cm9\,\text{cm}:\newlineThis pair cannot be proportional to the sides of rectangle A because the ratio of the sides of rectangle A is less than 22, and here the second side is much larger than the first, indicating a ratio greater than 22.\newlineTherefore, without calculation, we can conclude this pair is not a possible solution.

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