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# What is the least number of squares with area 9 to cover completely,

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Math Expert
Joined: 02 Sep 2009
Posts: 49272
What is the least number of squares with area 9 to cover completely,  [#permalink]

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02 Oct 2017, 11:22
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Difficulty:

15% (low)

Question Stats:

94% (00:33) correct 6% (00:11) wrong based on 36 sessions

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What is the least number of squares with area 9 to cover completely, without overlap, a square with side of length 9?

(A) 2
(B) 3
(C) 4
(D) 9
(E) 12

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What is the least number of squares with area 9 to cover completely,  [#permalink]

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02 Oct 2017, 13:09
Bunuel wrote:
What is the least number of squares with area 9 to cover completely, without overlap, a square with side of length 9?

(A) 2
(B) 3
(C) 4
(D) 9
(E) 12

Area:

The big square has area (9*9) = 81

The small squares have area 9

Larger area/ smaller areas = number of squares with the smaller area

81 / 9 = Answer D

Side length:

Small squares' area = 9. Their sides have a length of 3.

How many short lengths will fit into a longer length?

9 / 3 = 3 small side lengths fit without overlap into one side length

But they're two-dimensional squares. Area = Length times length. We have one length calculated. We need two. We have to consider a second side of the big square.

A second side: 9 / 3 = 3

Now multiply:

(# of small that fit on one side) * (# that fit on another side): 3 * 3 = 9

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Re: What is the least number of squares with area 9 to cover completely,  [#permalink]

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02 Oct 2017, 23:43
Bunuel wrote:
What is the least number of squares with area 9 to cover completely, without overlap, a square with side of length 9?

(A) 2
(B) 3
(C) 4
(D) 9
(E) 12

Area to be covered = Area of square with side 9 = 9^2 = 81

Area of squares to be used cover the bigger square = 9

Number of Smaller squares = Area of bigger square / Area of small square = 81/9 = 9

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Re: What is the least number of squares with area 9 to cover completely,  [#permalink]

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03 Oct 2017, 10:02
Area of square =9, so side=3. Now the overlapping square has side length of nine. So HCF of 3&9 is 3, so the smaller squares need to be of 3*3 size. Now with bigger square of length 9*9 would be 3 squares in columns and 3 squares in rows so total number of squares would 3*3=9 and answer is D

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Re: What is the least number of squares with area 9 to cover completely,  [#permalink]

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03 Oct 2017, 21:21
Total Area of Square to be Covered= 9*9

Total area of square which are used for covering purpose is 9

So number of square required for covering = 81/9 = 9
Re: What is the least number of squares with area 9 to cover completely, &nbs [#permalink] 03 Oct 2017, 21:21
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