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Re: Ramon wants to cut a rectangular board into identical square
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15 Dec 2022, 10:05
15 Dec 2022, 10:05
1
H.c.f/g.c.d of 18 and 30=6
Therefore a smaller square must have an area of 6×6=36
Number of small squares=(18×30)/36=15
Posted from my mobile device
Therefore a smaller square must have an area of 6×6=36
Number of small squares=(18×30)/36=15
Posted from my mobile device
Re: Ramon wants to cut a rectangular board into identical square
[#permalink]
04 Apr 2023, 05:47
04 Apr 2023, 05:47
1
The answers that make use of the GCF are very fantastic and is an important concept to know, however since it is not a numeric entry question, this is a question where you can work backwards to get the answer.
You can use this as a shortcut when you are pressed for time and can't seem to figure out what technique to use. We are looking for the least number of square pieces that can fit in this rectangle without any wastage, hence we are looking for the largest size of square pieces that will fit perfectly.
Step 1: Since the rectangle's lengths are 18 and 30, we can find the area of the rectangle to be 18 x 30 = 540.
Step 2: Next you can divide each answer choice to know which one gives you a perfect square.
Step 3: Even if you find a perfect square, you have to check all the answers to know which gives the biggest perfect square since we want to have the least number of square pieces.
(A) 4
540/4 = 135 (Not a perfect square)
(B) 6
540/6 = 90 (Not a perfect square)
(C) 9
540/9 = 60 (Not a perfect square)
(D) 12
540/12 = 45 (Not a perfect square)
(E) 15
540/15 = 36 (A perfect square) = Answer.
Please let me know if this answer helps by giving me a Kudos. I am still new here and I am preparing for the GRE exams. Thanks a lot!
You can use this as a shortcut when you are pressed for time and can't seem to figure out what technique to use. We are looking for the least number of square pieces that can fit in this rectangle without any wastage, hence we are looking for the largest size of square pieces that will fit perfectly.
Step 1: Since the rectangle's lengths are 18 and 30, we can find the area of the rectangle to be 18 x 30 = 540.
Step 2: Next you can divide each answer choice to know which one gives you a perfect square.
Step 3: Even if you find a perfect square, you have to check all the answers to know which gives the biggest perfect square since we want to have the least number of square pieces.
(A) 4
540/4 = 135 (Not a perfect square)
(B) 6
540/6 = 90 (Not a perfect square)
(C) 9
540/9 = 60 (Not a perfect square)
(D) 12
540/12 = 45 (Not a perfect square)
(E) 15
540/15 = 36 (A perfect square) = Answer.
Please let me know if this answer helps by giving me a Kudos. I am still new here and I am preparing for the GRE exams. Thanks a lot!
Re: Ramon wants to cut a rectangular board into identical square
[#permalink]
19 May 2024, 05:28
19 May 2024, 05:28
To solve this problem efficiently, let's lean on our understanding of divisibility.
We want to cut the rectangle into identical squares. We want the least number of squares that will fit exactly within the rectangle area.
We know therefore that each side length of the rectangle will be a multiple of the corresponding side length of that square.
In other words, the question asks what is the greatest common divisor of 18 and 30.
We want to cut the rectangle into identical squares. We want the least number of squares that will fit exactly within the rectangle area.
We know therefore that each side length of the rectangle will be a multiple of the corresponding side length of that square.
In other words, the question asks what is the greatest common divisor of 18 and 30.
