QR question

[299678]

What is the maximum number of 3 inch squares (squares that are 3 inches on a side) that can be cut from a sheet of tin 19 x 23 inches?

correct answer is 42. I need ur explanation. Thank you

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[Habbas]

Its relatively simple:

one side has a length of 19 inches meaning that out of that 6 squares could be cut with a 3 inch side (6 X 3 = 18).

On another side the length is 23 inches meaning that 7 squares could be cut with a 3 inch side (7 X 3 = 21).

Then 6 squares can be cut on one side X 7 squares on the other side = 42

 

[299678]

hmm. Thank you Habbas. Interesting solution. What I did was calculating the area and divide by 9, which gave me incorrect answer as 48, your explanation sounds logic to me, but I still don't understand why my calculation is wrong. Thank you

 

[oae]

The reason your answer is wrong is because your calculations uses the entire surface area. The questions asks how many perfect squares can you cut out. You can only cut out 42 perfect squares.

Your answer gives 48 because it assumes that all the excess foil scraps left over around the edges cannot be somehow combined to form more 3x3 squares. But you cannot do this.

Example
____________________
____________________

The above strip of foil is 10 inches long. 3 inches thick.

If you try to cut out "3x3" sqaures, then you'll get 3 perfect squares, with some foil left over on the end.

 

[299678]

Oh I see. Thank you Oae !