Given:

Length of stick S1 = 7.5 feet Length of stick S2 = 3.25 feet To determine the minimum length we can measure, we use stick S2 to measure the length of stick S1. By doing so, we get:

Total length of S1 = 3.25 + 3.25 + remaining length of S1 $6.5$ + remaining length of S1 = $7.5$ Therefore, the remaining length of S1 = $7.5 – 6.5 = 1$ foot Thus, the minimum length that can be measured is 1 foot.

Note: If the question had asked, "What are the minimum possible pieces of equal size that we can make by cutting the two sticks?", we would solve it as follows:

Length of stick S1 = 7.5 feet = $\frac{15}{2}$ feet Length of stick S2 = 3.25 feet = $\frac{13}{4}$ feet The maximum possible size of a piece would be the HCF of ($\frac{15}{2}$ and $\frac{13}{4}$):

HCF of (15, 13) = 1, and LCM of (2, 4) = 4 So, the maximum size of each piece = $\frac{1}{4}$ = 0.25 feet The number of minimum possible pieces of equal size is:

$(7.5 + 3.25) / 0.25 = 43$ pieces.