Question 15: A rectangular room is 680cm long and 480cm wide. They wanted to fill the room with square tiles without any of the tiles being cut off. What is the longest brick length?
Let the length of the brick be x.
To cover a room without any tiles being cut, x must be a divisor of the length and width of the room.
Or 680⋮x and 480⋮x
x∈ UCC(680;480)
Let x be the maximum ⇒x=GCLN(680;480)
We have: 680=23.5.17; 480=25.3.54
⇒x= UCLN(680;480)=23.5=40
So to cover the room without any mutilated bricks, the length of the largest brick side is 40 cm.
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