Question

To get to her parents' house, Francesca would have to drive due north 96 kilometers. To get to her grandparents' house, she would have to drive due east 28 kilometers. What is the straight-line distance between the parents' and grandparents' houses?

Answer 1

Answer: 100 kilometers

Step-by-step explanation:

1. draw a right angled triangle with the vertical line (line due north) as 96 km, and the horizontal line (line due east) as 28 km, and a hypotenuse, which we can label as c.

2. we can use the formula for a hypotenuse, the pythagorean theorem that
`a^(2) + b^2 = c^2`, where a and b are the sides and c is the hypotenuse.

3. substitute the values for a and b as 96 and 28,
`96^(2) +28^(2) = c^2\\10000 = c^2`

4. take the square root of both sides to solve for c,

`√(10000) = √(c^2)\\`

`100 = c`

therefore, as the square root of 10000 = c, c = 100