Question

From her house, Mabel could drive due north to get to her parents' house or she could drive due east to get to her grandparents' house. It is 2 miles from Mabel's house to her parents' house and a straight-line distance of 9 miles from her parents' house to her grandparents' house. How far is Mabel from her grandparents' house? If necessary, round to the nearest tenth.

Answer 1

Mabel is approximately 9.2 miles from her grandparents' house.

To find the distance from Mabel's house to her grandparents' house, we can use the Pythagorean Theorem since Mabel would have formed a right-angled triangle with her house, her parents' house, and her grandparents' house.

Let's denote the distance from Mabel's house to her parents' house as
`\( a \)`, the distance from her parents' house to her grandparents' house as
`\( b \)`, and the distance from Mabel's house to her grandparents' house as
`\( c \)`.

According to the Pythagorean Theorem:

`\[ c^2 = a^2 + b^2 \]`

Given that a = 2 miles and b = 9 miles:

`\[ c^2 = 2^2 + 9^2 \]`

`\[ c^2 = 4 + 81 \]`

`\[ c^2 = 85 \]`

Now, take the square root of both sides to find
`\( c \)`:

`\[ c = √(85) \]`

Using a calculator, we get approximately
`\( c \approx 9.2 \)` miles.

Therefore, Mabel is approximately 9.2 miles from her grandparents' house. Rounded to the nearest tenth, the distance is 9.2 miles.