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?
To find out how many miles Elena needs to drive to get from home to work, we can use the Pythagorean theorem. We know that Elena's office is 25 miles southeast of her home. In a right triangle, the hypotenuse is the longest side and it represents the distance traveled. The other two sides represent the distances traveled in each direction (south and east).
Let's assume Elena needs to drive x miles south and y miles east. According to the Pythagorean theorem, the sum of the squares of the two shorter sides (x^2 + y^2) is equal to the square of the hypotenuse (25^2):
x^2 + y^2 = 25^2
In this case, since Elena needs to drive southeast (both south and east), we can use the Pythagorean triple (7, 24, 25) to find the values of x and y. The triple means that 7 is the distance traveled south, 24 is the distance traveled east, and 25 is the hypotenuse (total distance traveled).
So, Elena needs to drive 7 miles south and 24 miles east to get from home to work using the Pythagorean triple (7, 24, 25).