The distance between the library and the park can be found using the Pythagorean theorem:
(library-park)^2 = (library-home)^2 - (home-park)^2
(library-park)^2 = 12^2 - 9^2
(library-park)^2 = 144 - 81
(library-park)^2 = 63
library-park = square root of 63 = square root of (3 * 3 * 7) = 3 * square root of 7
So, the library is 3 times the square root of 7 miles away from the park.
The distance between the park and the football field can be found using the Pythagorean theorem as well:
(park-football field)^2 = (home-football field)^2 - (home-park)^2
(park-football field)^2 = 12^2 - 9^2
(park-football field)^2 = 144 - 81
(park-football field)^2 = 63
park-football field = square root of 63 = square root of (3 * 3 * 7) = 3 * square root of 7
So, the park is also 3 times the square root of 7 miles away from the football field.
Kathy lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kathy’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 9 miles from her home. The football field is 12 miles from the library. The vertex at the lower left is labeled 'Football field.' The vertex at the upper right is labeled 'Home.' The vertex at the upper left is labeled 'Park' and is marked with a small square. A line segment connects the upper left vertex to the hypotenuse at a point that is labeled 'Library.' The angle formed by the hypotenuse and the line segment is marked with a small square. The distance between the football field and library is labeled 12 miles. The distance between the library and home is labeled 9 miles. How far is the library from the park? How far is the park from the football field? (1 point) Responses miles; miles Image with alt text: 6 square root 3 miles; Image with alt text: 6 square root 7 miles miles; miles Image with alt text: 6 square root 7 miles; Image with alt text: 6 square root 3 miles miles, miles Image with alt text: square root 33 miles, Image with alt text: square root 21 miles miles, miles Image with alt text: square root 21 miles, Image with alt text: square root 33 miles Skip to navigation
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