Question

a lawyer drives from her home, located 7 miles east and 21 miles north of the town courthouse, to her office, located 3 miles west and 3 miles south of the courthouse. find the distance between the lawyers home and her office. the distance between her home and her office is \\(\square\\) miles. (type an integer or a decimal.)

Explanation:

Step1: Calculate east-west distance difference

The home is 7 miles east of the courthouse, the office is 3 miles west of the courthouse. Total east-west distance between home and office:
$7 + 3 = 10$ miles

Step2: Calculate north-south distance difference

The home is 21 miles north of the courthouse, the office is 3 miles south of the courthouse. Total north-south distance between home and office:
$21 + 3 = 24$ miles

Step3: Apply Pythagorean theorem

The straight-line distance is the hypotenuse of a right triangle with legs 10 and 24.

$$ \text{Distance} = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} $$

Step4: Compute the square root

$\sqrt{676} = 26$

Answer:

26