T. 5 Pythagorean theorem: word problems 87 U To get to her parents' house, Leslie would have to drive due north 9 kilometers. To get to her grandparents' house, she would have to drive due east 12 kilometers. What is the straight- line distance between the parents' and grandparents' houses?

To find the straight-line distance between the parents' and grandparents' houses, we can use the Pythagorean theorem. Given: - Distance due north to the parents' house = 9 km - Distance due east to the grandparents' house = 12 km We can use the Pythagorean theorem to find the straight-line distance between the two houses. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Let's denote the straight-line distance between the parents' and grandparents' houses as \(d\). Using the Pythagorean theorem: \[ d^2 = 9^2 + 12^2 \] Now, we can calculate the value of \(d\). Calculate the value by following steps: - step0: Calculate: \(9^{2}+12^{2}\) - step1: Evaluate the power: \(81+12^{2}\) - step2: Evaluate the power: \(81+144\) - step3: Add the numbers: \(225\) The square of the straight-line distance between the parents' and grandparents' houses is 225. To find the straight-line distance, we take the square root of 225: \[ d = \sqrt{225} = 15 \text{ km} \] Therefore, the straight-line distance between the parents' and grandparents' houses is 15 kilometers.