Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’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 6 miles from her home. The football field is 8 miles from the library.

Question

How far is the library from the park? How far is the park from the football field?
√22 miles; 2√10 miles
2√10 miles; √22 miles
6√2 miles; 6√11 miles
6√11 miles; 6√2 miles

Answer 1

I think it's C, but I'm not sure. Is that correct?

Answer 2

How far is the library from the park?
x^2 = 6*8

I don't see that as a choice.

??

Answer 3

hmmm... I'm a bit confused. could you help me out with just how to set the equation up?

Answer 4

it is well known that the altitude of a right triangle is the geometric mean of the two parts of the hypotenuse.

See, for example,

http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/rightday3.html

Answer 5

ohhh... so how would I use that information to help me get to the answer?