Question

what is the greatest possible length of the scale to measure exactly the following lengths 20 feet 13 feet 9 inches 17 feet 66 inches 21 feet 3 inches​

Answer 1

ANSWER : 1 feet 3 inch

SOLUTION :

Given lengths are

20' = 240" (1 feet = 12 inch)

13' 9" = 165"

17' 6" = 210"

21' 3" = 255"

HCF of all above = 15" = 1' 3"

So, Scale length must be 1 feet 3 inch

Answer 2

Answer:

The greatest possible length of the scale to measure these lengths exactly is 15 inches.

Step-by-step explanation:

Given Data:

The given lengths are 20 feet 13 feet 9 inches 17 feet 66 inches 21 feet 3 inches​

To Find:

The greatest possible length that can be used to measure all the given measurements.

Calculations:

To find the greatest possible length of the scale, we need to find the highest common factor (HCF) of all the given lengths in feet and inches.

First, let's convert all lengths to inches:

20 feet = 240 inches

13 feet 9 inches = 165 inches

17 feet 66 inches = 258 inches

21 feet 3 inches = 255 inches

Now, we can find the HCF of these lengths by prime factorizing each number and finding the common factors:

240 = $2^{4}$ × 3 × 5

165 = 3 × 5 × 11

258 = 2 × 3 × 43

255 = 3 × 5 × 17

The common factors are 3 and 5, so the HCF is 3 × 5 = 15 inches.

Therefore, the greatest possible length of the scale to measure these lengths exactly is 15 inches.

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