Atree farm, located on a rectangular landmass, currently has 162,981 trees on it. at opposite corners of the farm, there are check-in stations 20 miles apart, as shown below.

if α measures 60°, what is the approximate density of trees on the farm?

a. 173 trees per square mile
b. 815 trees per square mile
c. 471 trees per square mile
d. 941 trees per square mile

Option D. 941 trees per square mile

Step-by-step explanation:

Let

x> the length of the farm

y> the width of the farm

step 1

Find the value of y

we know that

Remember that

so

step 2

Find the value of x

we have

substitute the values

step 3

Find the area of the farm

step 4

Find the density of trees on the farm

Divide the number of trees by the total area

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl