Final answer:
Using the Pythagorean theorem, we find the diagonal path is 25 feet. The original path was 35 feet. The diagonal path would therefore be 10 feet shorter.
Step-by-step explanation:
To determine how much shorter it would be if the student could cut across a neighbor's yard on a diagonal to her friend's house, we can use the Pythagorean theorem. The student's path makes a right triangle with one leg measuring 20 feet (the distance to the corner) and the other leg measuring 15 feet (the distance from the corner to the friend's house). We calculate the hypotenuse (the diagonal distance) using the formula c = \(\sqrt{a^2 + b^2}\), where c is the hypotenuse and a and b are the legs of the triangle. Plugging in the values, we get c = \(\sqrt{20^2 + 15^2}\) = \(\sqrt{400 + 225}\) = \(\sqrt{625}\) = 25 feet. The original path was 20 feet to the corner plus 15 feet to the friend's house, totaling 35 feet. Subtracting the diagonal distance (25 feet) from the original path (35 feet) gives us 10 feet. Therefore, the correct answer is not listed in the options provided. If she could walk diagonally, the path would be 10 feet shorter.