Final answer:
Using the Pythagorean theorem on the right triangle formed by Alexa's, her parents', and her grandparents' houses, the distance from Alexa's house to her grandparents' house is found to be approximately 25.6 kilometers.
Step-by-step explanation:
To determine the distance from Alexa's house to her grandparents' house, we can visualize this scenario as a right triangle where Alexa's house is one vertex, her parent's house is another vertex (16 kilometers due north), and her grandparents' house is the third vertex (20 kilometers east from her parent's house). Because these distances form a right triangle, we can use the Pythagorean theorem to find the distance between Alexa's house and her grandparents' house.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This is written as:
a² + b² = c²
Here, a is 16 km (north direction), b is 20 km (east direction). Squaring both sides gives us:
16² + 20² = c²
which calculates to:
256 km² + 400 km² = c²
Adding these together provides:
656 km² = c²
Taking the square root of both sides to find c, we get:
√656 km² = c
c ≈ 25.6 km
Thus, the distance from Alexa's house to her grandparents' house is approximately 25.6 kilometers, which is none of the options listed; it is a new option (e) 25.6 kilometers.