SOLUTION: you have a wooden board that measures 54 cm by 90 cm. you want to cut the board into identical square pieces with integer side lengths and use all of the wood

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Question 762963: you have a wooden board that measures 54 cm by 90 cm. you want to cut the board into identical square pieces with integer side lengths and use all of the wood
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Area for the rectangular form of board is 54*90=27*2*9*2*5=3*3*3*2*3*3*2*5=3^5 * 2^2 * 5 =9*2*sqrt(15)=18*sqrt(15)
54: 3%2A3%2A3%2A2
90: 3%2A3%2A2%2A5
Common factor is 2*3*3=18
90%2F18=5
54%2F18=3
The noncommon factors may give what we want.

324%2A15=54%2A90=4860
324 squares of side 15 cm each