2017 AMC 10A Problem 7

The answer is a percent, so the size of the field does not change it. Pick the easiest size: each side is $1$.

1. Jerry's trip. He walks one full side east and one full side north: $1 + 1 = 2$.
2. Silvia's trip. She walks straight across the square, corner to corner. That diagonal is the long side of a right triangle whose two short sides are both $1$. By the Pythagorean theorem,
$$\text{diagonal} = \sqrt{1^2 + 1^2} = \sqrt{2} \approx 1.414.$$
3. How much shorter. $2 - 1.414 = 0.586$.
4. As a percent. "Shorter compared to Jerry's trip" means divide by Jerry's distance:
$$\frac{0.586}{2} \approx 0.293 = 29.3\%.$$
5. The closest choice is $30\%$.

The answer is $\boxed{\textbf{(A)}\ 30\%}$.

When every answer is a percent, choose simple numbers for the lengths; the percent comes out the same for any size. A percent decrease is always measured against the starting amount, here Jerry's longer trip. It also helps to remember $\sqrt{2} \approx 1.414$, the diagonal of a square with side $1$.

The size of the field does not matter, so let each side be $1$.

Jerry walks two full sides: $1 + 1 = 2$.

Silvia walks the diagonal, the hypotenuse of a right isosceles triangle with legs $1$, so her distance is $\sqrt{1^2 + 1^2} = \sqrt{2} \approx 1.414$.

She saves $2 - 1.414 = 0.586$, which as a fraction of Jerry's trip is
$$\frac{0.586}{2} \approx 0.293 \approx 29\%.$$

The closest choice is $\boxed{\textbf{(A)}\ 30\%}$.