Problem Description:
The image shows a right triangle formed by three streets: A street, B street, and C street. The distance between Ram's house and Sita's house is represented by the hypotenuse of the triangle (C street). The legs of the triangle are:
- A street: 2 miles (horizontal distance)
- B street: 1.5 miles (vertical distance)
The task is to determine the length of C street, which is the direct distance between Ram's house and Sita's house.
---
Solution Approach:
To solve this problem, we will use the
Pythagorean theorem, which states that in a right triangle:
\[
c^2 = a^2 + b^2
\]
where:
- \( c \) is the length of the hypotenuse (the side opposite the right angle),
- \( a \) and \( b \) are the lengths of the other two sides (the legs of the triangle).
In this problem:
- \( a = 2 \) miles (length of A street),
- \( b = 1.5 \) miles (length of B street),
- \( c \) is the length of C street, which we need to find.
---
Step-by-Step Calculation:
1.
Identify the given values:
\[
a = 2 \quad \text{and} \quad b = 1.5
\]
2.
Apply the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Substitute the values of \( a \) and \( b \):
\[
c^2 = 2^2 + 1.5^2
\]
3.
Calculate \( a^2 \) and \( b^2 \):
\[
2^2 = 4
\]
\[
1.5^2 = 2.25
\]
4.
Add the squares:
\[
c^2 = 4 + 2.25 = 6.25
\]
5.
Take the square root to find \( c \):
\[
c = \sqrt{6.25}
\]
\[
c = 2.5
\]
---
Final Answer:
The length of C street, which is the direct distance between Ram's house and Sita's house, is:
\[
\boxed{2.5}
\] miles.
Parent Tip: Review the logic above to help your child master the concept of real life pythagorean theorem examples.
