Question

Use the map to answer the question.
Information
Short description, A map.,Long description,
A map shows the distance between Maria’s house, Jon’s house, and school. These locations form the points of a right triangle. School is at the right angle. From John’s house to school is 5 miles. From Maria’s house to school is 4 miles. From Jon’s house to Maria’s house is X, the hypotenuse.
Question
What is the distance, x, between Jon's house and Maria's house?

Answer 1

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.