A rectangular piece of wood measures 3.48m by 2.28m. Ali wishes to cut squares of the largest possible size from it without any leftover. What is the length of each square piece?
convert to cm
the piece is 348 cm by 228 cm
for an area of
79344 cm^2
79344 = 16x9x551 or 551 x (144)
so he can cut 551 squares , each one being 12 cm by 12 cm
(Two things I see wrong with this question.
1. That is one very large piece of wood, never seen one that big , the largest sheet of wood I can get at my lumber yard is 4 by 8 ft which is appr. 122 cm by 244 cm
2. How could he make all those cuts without losing anything to sawcuts ?)
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To cut squares of the largest possible size from the rectangular piece of wood without any leftover, you need to find the greatest common divisor (GCD) of the lengths of the rectangle.
The dimensions of the rectangle are 3.48m by 2.28m.
To find the GCD, you can simplify the dimensions of the rectangle by dividing them by their common denominator (in this case, 0.12m).
The simplified dimensions of the rectangle are 29 by 19.
Now, you can find the GCD of 29 and 19 using a method like Euclid's algorithm.
Divide 29 by 19: 29 ÷ 19 = 1 remainder 10.
Since there is a remainder, divide 19 by 10: 19 ÷ 10 = 1 remainder 9.
Divide 10 by 9: 10 ÷ 9 = 1 remainder 1.
Finally, divide 9 by 1: 9 ÷ 1 = 9.
The GCD of 29 and 19 is 9.
Now, convert this back to the original units by multiplying the GCD by the common denominator (0.12m):
9 × 0.12m = 1.08m
Therefore, the length of each square piece is 1.08m.