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Ramon wants to cut a rectangular board into identical square
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12 Aug 2018, 15:33
12 Aug 2018, 15:33
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Question Stats:
57% (01:37) correct
42% (01:46) wrong based on 311 sessions
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Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
Re: Ramon wants to cut a rectangular board into identical square
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15 Aug 2018, 05:20
15 Aug 2018, 05:20
5
Expert Reply
Explanation
Cutting a rectangular board into square pieces means that Ramon needs to cut pieces that are equal in length and width. “Without wasting any of the board” means that he needs to choose a side length that divides evenly into both 18 and 30.
“The least number of square pieces” means that he needs to choose the largest possible squares. With these three stipulations, choose the largest integer that divides evenly into 18 and 30, or the greatest common factor, which is 6. This would give Ramon 3 pieces going one way and 5 pieces going the other.
He would cut 3 × 5 = 15 squares of dimension 6" × 6". Note that this solution ignored squares with non-integer side length for the sake of convenience, a potentially dangerous thing to do. (After all, identical squares of 1.5" by 1.5" could be cut without wasting any of the board.) However, to cut squares any larger than 6" × 6", Ramon could only cut 2 squares of 9" or 1 square of 18" from the 18" dimension of the rectangle, neither of which would evenly divide the 30" dimension of the rectangle. The computed answer is correct.
Cutting a rectangular board into square pieces means that Ramon needs to cut pieces that are equal in length and width. “Without wasting any of the board” means that he needs to choose a side length that divides evenly into both 18 and 30.
“The least number of square pieces” means that he needs to choose the largest possible squares. With these three stipulations, choose the largest integer that divides evenly into 18 and 30, or the greatest common factor, which is 6. This would give Ramon 3 pieces going one way and 5 pieces going the other.
He would cut 3 × 5 = 15 squares of dimension 6" × 6". Note that this solution ignored squares with non-integer side length for the sake of convenience, a potentially dangerous thing to do. (After all, identical squares of 1.5" by 1.5" could be cut without wasting any of the board.) However, to cut squares any larger than 6" × 6", Ramon could only cut 2 squares of 9" or 1 square of 18" from the 18" dimension of the rectangle, neither of which would evenly divide the 30" dimension of the rectangle. The computed answer is correct.
Re: Ramon wants to cut a rectangular board into identical square
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03 Sep 2018, 00:38
03 Sep 2018, 00:38
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Another approach:
The area of the rectangle is 18*30 = 540
Area of any square =x^2
Now we are required to find the least number of squares that fit exactly inside the rectangle.
Form a equation nx^2 = 540
Replace ans choices for n, when n = 15 the equation reduces to x^2 = 36 therefore each square will be of side 6.
For all other values of n x will not be an integer hence there will be some wastage of board.
The area of the rectangle is 18*30 = 540
Area of any square =x^2
Now we are required to find the least number of squares that fit exactly inside the rectangle.
Form a equation nx^2 = 540
Replace ans choices for n, when n = 15 the equation reduces to x^2 = 36 therefore each square will be of side 6.
For all other values of n x will not be an integer hence there will be some wastage of board.
