I want to cut 10 identical rectangles each 6 cm x 10 cm, from rectangular plastic boards that are 15 cm x 20 cm. Each of the 10 rectangles must be cut out as one piece - joins are not allowed.What is the smallest number of plastic boards that I can use?
Correct answer: B. 3
- A. 2
- B. 3
- C. 4
- D. 5
Explanation
To cut 10 identical rectangles, each measuring 6 cm x 10 cm, we need a total of 600 cm² of material.Each plastic board has an area of 15 cm x 20 cm = 300 cm². Therefore, we need to calculate the total area of the material required to cut out 10 rectangles.To obtain a total area of 600 cm² (for 10 rectangles), we need at least 2 plastic boards. However, cutting out 6 rectangles from each of these two boards would require overlapping cuts, which is not allowed.From each 15 cm x 20 cm board, we can cut out only 4 rectangles without overlapping cuts. In order to get 10 rectangles, we need a minimum of three plastic boards to obtain 10 rectangles without any overlapping cuts.Therefore, the correct answer is B) 3.
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