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Complete the explanation of why it is possible to draw more than two different rectangles with an area of 100 square units, but it is not possible to draw more than two rectangles with an area of 15 square units. The lengths of the sides of the rectangle are whole numbers. 100 has factor pairs, so that many different rectangles can be drawn. 15 only has factor pairs, so only that many different rectangles can be drawn.

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Answer:

100 has 5 factor pairs, so that many different rectangles can be drawn. 15 only has 2 factor pairs, so only that many different rectangles can be drawn.

Explanation:

there are 5 pairs of whole numbers that multiplied together will be 100:

  1. 100 x 1 = 100
  2. 50 x 2 = 100
  3. 25 x 4 = 100
  4. 20 x 5 = 100
  5. 10 x 10 = 100

while there are only 2 pairs of whole numbers that multiplied together will be 15:

  1. 15 x 1 = 15
  2. 3 x 5 = 15

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