County x has a population density of 250 people per square mile. the total
population of the county is 150,000. which geometric model could be the shape of
county x?
a a parallelogram with a base of 25 miles and a height of 25 miles
b a rectangle that is 15 miles long and 45 miles wide
c a right triangle with a leg that is 30 miles long and a hypotenuse that is
50 miles long
d a trapezoid with base lengths of 10 miles and 30 miles and a height of
25 miles

Option C. is the correct option.

Step-by-step explanation:

County X has a population density of 250 people per square mile.

Total population of the county is 150000.

Total area which represents the population = = square mile.

So geometric model which has the same area as 600 square miles will be the answer.

A). Area of a parallelogram = Base × height

= 25×25

= 625 square miles

which is not equal to 600 square miles so it's not the correct option.

B). Area of a rectangle = Length×width

= 15×45 = 675 square miles ≠ 600 square miles

Therefore, not the correct option.

C). Area of a right triangle =

Since length of hypotenuse is given so we will find the length of height.

Height = √[(Hypotenuse)²- (Base)²] =

=

=

= 40 miles

So area of the right triangle =

=

= 600 square miles

Which matches the area of County X, so it's a correct option.

D). area of trapezoid =

=

=

= 20×25

= 500 square miles ≠ 600 miles

Therefore, this option is not correct.