To find the distance \( X \) between Jon's house and Maria's house, we can use the Pythagorean theorem. In a right triangle, the sum of the squares of the two legs (the shorter sides) equals the square of the hypotenuse (the longest side).
Here, we have:
- From Jon's house to the school (one leg) = 5 miles
- From Maria's house to the school (another leg) = 4 miles
- From Jon's house to Maria's house (the hypotenuse) = \( X \)
According to the Pythagorean theorem:
\[ X^2 = (5 \text{ miles})^2 + (4 \text{ miles})^2 \]
Calculating the squares:
\[ X^2 = 25 + 16 \]
\[ X^2 = 41 \]
Now, taking the square root of both sides to find \( X \):
\[ X = \sqrt{41} \]
Thus, the distance between Jon's house and Maria's house is \( \sqrt{41} \) miles, which is approximately 6.4 miles.