help with this geometry puzzle

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nanase

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Aug 8, 2019
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John wants to cut the biggest possible squares from a rectangular sheet of paper without any leftover paper. The sheet of paper has a length of 65cm and breadth of 50cm.
a. what is the length of each square?
b. how many squares can he cut altogether?

what I've done:

I tried using grid paper, and did several trial and error, but there is always some left over, did I miss something here? pls help
 
when i drew it in grid of 5x5 cm, i could get 130 squares, but is it really that simple or is there any other solution of squares with different sides that can fit exactly like puzzle? I feel like this is a trick question
 
Off the top of my head I'd cut off the largest square (which is the square containing the smaller side) from the remaining rectangle at each stage until the remaining rectangle has square shape.
 
nanaseailie said:
John wants to cut the biggest possible squares from a rectangular sheet of paper without any leftover paper. The sheet of paper has a length of 65cm and breadth of 50cm.
a. what is the length of each square?
b. how many squares can he cut altogether?

what I've done:

I tried using grid paper, and did several trial and error, but there is always some left over, did I miss something here? pls help
Click to expand...
Are the squares supposed to be all the same size, or are we looking for a set of different squares? (I see that @blamocur is assuming the latter.)

nanaseailie said:
when i drew it in grid of 5x5 cm, i could get 130 squares, but is it really that simple or is there any other solution of squares with different sides that can fit exactly like puzzle? I feel like this is a trick question
Click to expand...
That is likely to be the answer, assuming the squares are to be the same size; this is an exercise in using the GCD. Do you see why, and why it is not necessary to draw anything?
 
nanaseailie said:
when i drew it in grid of 5x5 cm, i could get 130 squares, but is it really that simple or is there any other solution of squares with different sides that can fit exactly like puzzle? I feel like this is a trick question
Click to expand...
Just take each of your 130 squares and divide them into 4 equal areas or divide them into 16=4^2 equal areas or divide them in 64=4^3 equal areas or ....
Is this what you mean? Of course, these will not yield the largest possible squares.
 
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