Question

help?

Answer 1

@agent0smith

Answer 2

According to ur figure square of distance from library to park is the product of distance from library to football field and distance from library to home.
from this u can find the distance of library from park.
After this using pythagorean theorem u can find out the distance between park and football field.

Answer 3

Geometric mean.

Answer 4

so the answer is the 1st option.

Answer 5

http://www.regentsprep.org/Regents/math/geometry/GP12/LMeanP.htm

Answer 6

Or: http://www.cliffsnotes.com/math/geometry/right-triangles/altitude-to-the-hypotenuse

Answer 7

A:
Let the distance between park and library be X units, hence using geometric mean property we have;
\[\huge X^2 = 12 \times 9\]
\[\huge \rightarrow X = \sqrt{12 } \times \sqrt 9\]
\[\huge \rightarrow X = 2\sqrt{3 } \times 3 = 6\sqrt{3 }\]
\[\huge \rightarrow X = 6\sqrt{3 }\]
Hence library is 6√3 miles from the park.

B:
Now let us consider the right triangle formed by the vertices park, library and football field
Let the distance from park to football field be Y miles, hence
by Pythagoras theorem we have;
\[\huge Y^2= 12^2 + (6\sqrt3)^2\]
\[\huge \rightarrow Y^2= 144 + 36 \times 3\]
\[\huge \rightarrow Y^2= 144 + 108=252\]
\[\huge \rightarrow Y^2=252\]
\[\huge \rightarrow Y=\sqrt{252}\]
\[\huge \rightarrow Y=\sqrt{36 \times 7}\]
\[\huge \rightarrow Y=6\sqrt{7}\]

Hence the distance from park to football field is 6√7miles
thus first option is the correct answer.

@abbie