Which greatest possible length can be used to measure exactly 15 meter 75 cm,…
2024
Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7 meter 65 cm
Answer: B. 45 — Convert to centimeters: convert all lengths to cm. 15 m 75 cm = 1575 cm 11 m 25 cm = 1125 cm 7 m 65 cm = 765 cm Find the greatest common divisor (GCD): use…
- A.
255
- B.
45
- C.
55
- D.
36
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Correct answer: B
Convert to centimeters: convert all lengths to cm.
15 m 75 cm = 1575 cm
11 m 25 cm = 1125 cm
7 m 65 cm = 765 cm
Find the greatest common divisor (GCD): use the Euclidean algorithm on 1575, 1125 and 765.
gcd(1575, 1125): 1575 − 1125 = 450 → gcd(1125, 450)
gcd(1125, 450): 1125 − 2×450 = 225 → gcd(450, 225)
gcd(450, 225): 450 − 2×225 = 0 → gcd(1575,1125) = 225
Now gcd(225, 765): 765 − 3×225 = 90 → gcd(225, 90)
225 − 2×90 = 45 → gcd(90, 45)
90 − 2×45 = 0 → gcd(1575,1125,765) = 45
Answer: The greatest length that measures all three exactly is 45 cm.