If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure?

The correct option is 0.25 foot.

Step-by-Step Explanation:

To find the minimum non-zero length that can be measured using two straight sticks of length 7.5 feet and 3.25 feet, we need to find the Greatest Common Divisor (GCD) of the two lengths.

First, let us convert the lengths from decimal form into fractional form or express them in a common unit to easily compute the Greatest Common Divisor.

Converting the lengths into fractions:
First stick length = 7.5 feet = $\frac{15}{2}$ feet = $\frac{30}{4}$ feet
Second stick length = 3.25 feet = $\frac{13}{4}$ feet

Alternatively, we can express both lengths in terms of hundredths of a foot (or multiply by 100 to remove decimals):
7.5 × 100 = 750
3.25 × 100 = 325

Now, let us find the GCD of 750 and 325 using prime factorization or Euclid's algorithm:

750 = 2 × 3 × 5³
325 = 5² × 13

The common prime factor is 5² = 25.

So, GCD(750, 325) = 25.

Dividing back by 100 to get the length in feet:
Minimum measurable length = $\frac{25}{100}$ = 0.25 foot.

Therefore, the minimum length that can be measured using these two sticks is 0.25 foot.