Question

To get to her parents’ house, Mackenzie would have to drive due north 21 kilometers. To get to her grandparents’ house, she would have to drive due east 20 kilometers. What is the straight-line distance between the parents’ and grandparents’ houses?

Answer 1

The straight-line distance between Mackenzie's parents' and grandparents' houses is 29 kilometers, calculated using the Pythagorean theorem with the given distances of 21 kilometers north and 20 kilometers east as legs of a right-angled triangle.

Step-by-step explanation:

To calculate the straight-line distance between Mackenzie's parents' and grandparents' houses, we can use the Pythagorean theorem. Since she would have to drive 21 kilometers north to her parents' house and then 20 kilometers east to her grandparents' house, we can consider this scenario as a right-angled triangle with the two legs measuring 21 kilometers and 20 kilometers. The hypotenuse of this triangle would be the straight-line distance between the two houses.

The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
c2 = a2 + b2.
Substituting the values:

c2 = 212 + 202
= 441 + 400
= 841.

Now, we take the square root of both sides to find c:

c = √841
= 29 kilometers.

Therefore, the straight-line distance between the parents' and grandparents' houses is 29 kilometers.