Question
Suppose your school is located 1.2 miles south of your home. The mall is located 3.2 miles west of the school. What is the shortest distance between your home and the mall? Round to the nearest hundredth. Enter your answer in the box.
miles
miles
Answers
GPT-4o mini
To find the shortest distance between your home and the mall, we can use the Pythagorean theorem.
1. You are 1.2 miles south of your home, and the mall is located 3.2 miles west of the school. This creates a right triangle where one leg is the distance south from your home to the school (1.2 miles), and the other leg is the distance west from the school to the mall (3.2 miles).
2. We can now denote:
- \( a = 1.2 \) miles (south)
- \( b = 3.2 \) miles (west)
3. The length of the hypotenuse \( c \) (the shortest distance between your home and the mall) can be calculated using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
4. Plugging in the values:
\[
c = \sqrt{(1.2)^2 + (3.2)^2}
\]
\[
= \sqrt{1.44 + 10.24}
\]
\[
= \sqrt{11.68}
\]
\[
\approx 3.42
\]
Thus, the shortest distance between your home and the mall is approximately **3.42 miles**.
1. You are 1.2 miles south of your home, and the mall is located 3.2 miles west of the school. This creates a right triangle where one leg is the distance south from your home to the school (1.2 miles), and the other leg is the distance west from the school to the mall (3.2 miles).
2. We can now denote:
- \( a = 1.2 \) miles (south)
- \( b = 3.2 \) miles (west)
3. The length of the hypotenuse \( c \) (the shortest distance between your home and the mall) can be calculated using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
4. Plugging in the values:
\[
c = \sqrt{(1.2)^2 + (3.2)^2}
\]
\[
= \sqrt{1.44 + 10.24}
\]
\[
= \sqrt{11.68}
\]
\[
\approx 3.42
\]
Thus, the shortest distance between your home and the mall is approximately **3.42 miles**.