Question

page 15 of 15 Pythagorean Triples Quick Check 5 of 55 of 5 Items Question Elena’s office is 25 miles southeast of her home. Which of the following correctly uses a Pythagorean triple to find out how many miles Elena needs to drive south and then east to get from home to work?(1 point) Responses 5 miles south and 20 miles east 5 miles south and 20 miles east 7 miles south and 24 miles east 7 miles south and 24 miles east 7 miles south and 18 miles east 7 miles south and 18 miles east 5 miles south and 24.5 miles east 5 miles south and 24.5 miles east Skip to navigation

Answer 1

To determine the correct Pythagorean triple that represents the scenario where Elena's office is 25 miles southeast of her home, we are looking for a right triangle where the length of the hypotenuse is 25 miles.

The Pythagorean theorem states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \):

\[ a^2 + b^2 = c^2 \]

Given \( c = 25 \), we need to find integer values \( a \) and \( b \) that satisfy the equation:

\[ a^2 + b^2 = 25^2 \] \[ a^2 + b^2 = 625 \]

Now, let's check the options for the correct pairs \( (a, b) \):

1. 5 miles south and 20 miles east:
   \[ 5^2 + 20^2 = 25 + 400 = 425 \quad (\text{Not correct}) \]

2. 7 miles south and 24 miles east:
   \[ 7^2 + 24^2 = 49 + 576 = 625 \quad (\text{Correct!}) \]

3. 7 miles south and 18 miles east:
   \[ 7^2 + 18^2 = 49 + 324 = 373 \quad (\text{Not correct}) \]

4. 5 miles south and 24.5 miles east:
   \[ 5^2 + 24.5^2 = 25 + 600.25 = 625.25 \quad (\text{Not correct}) \]

Based on this analysis, the correct response is: 7 miles south and 24 miles east.