Question

From his home, Nolan would have to walk due north to get to his friend Mona's house and due east to get to his friend Zachary's house. It is 3 kilometers from Nolan's house to Zachary's house and a straight-line distance of 5 kilometers from Mona's house to Zachary's house. How far is Nolan's house from Mona's house?

Answer 1

To find the distance between Nolan's house and Mona's house, we can use the Pythagorean theorem since the paths from Nolan's house to Zachary's house and from Mona's house to Zachary's house form a right triangle.

Let's denote the distance between Nolan's house and Mona's house as "d".

According to the given information:
- The distance from Nolan's house to Zachary's house (adjacent side of the right triangle) is 3 kilometers.
- The distance from Mona's house to Zachary's house (opposite side of the right triangle) is 5 kilometers.

Using the Pythagorean theorem, the hypotenuse (d) can be calculated:

d^2 = (3^2) + (5^2)
d^2 = 9 + 25
d^2 = 34

Taking the square root of both sides:

d ≈ √34

Therefore, Nolan's house is approximately √34 kilometers away from Mona's house.