Answer:
The total length of the Dogwood Trail is 24 kilometers
The difference between the lengths of the trails is 6 kilometers
Step-by-step explanation:
The complete and correct question is
The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.
Which of the following statements are true about the lengths of the trails? Check all that apply.
1.The total length of the Dogwood Trail is 16 kilometers.
2.The total length of the Dogwood Trail is 24 kilometers.
3.The Elm Trail is longer than the Dogwood Trail.
4.The difference between the lengths of the trails is 2 kilometers.
5.The difference between the lengths of the trails is 6 kilometers.
The picture in the attached figure
step 1
Find the value of a
Applying the Pythagorean Theorem in the right triangle ABC
[tex]13^2=a^2+5^2\\a^2=169-25\\a^2=144\\a=12\ km[/tex]
step 2
Find the value of b
Applying the Pythagorean Theorem in the right triangle CDE
[tex]5^2=b^2+3^2\\b^2=25-9\\b^2=16\\b=4\ km[/tex]
step 3
Find the total length of the Dogwood Trail (solid blue line)
The total length is equal to
[tex]AD=AB+BC+CE+ED[/tex] ---> by segment addition postulate
substitute the given values
[tex]AD=a+5+b+3=(a+b+8)\ km[/tex]
substitute the value of a and b
[tex]AD=(12+4+8)=24\ km[/tex]
step 4
Find the total length of the Elm Trail (dashed red line)
The total length is equal to
[tex]AD=AC+CD[/tex] ---> by segment addition postulate
substitute the given values
[tex]AD=13+5=18\ km[/tex]
Verify the following statements
Part 1) The total length of the Dogwood Trail is 16 kilometers
The statement is false
Because
The total length of the Dogwood Trail is 24 kilometers (see the explanation)
Part 2) The total length of the Dogwood Trail is 24 kilometers
The statement is true (see the explanation)
Part 3) The Elm Trail is longer than the Dogwood Trail
The statement is false
Because
The Elm Trail is smaller than the Dogwood Trail
[tex]18\ km < 24\ km[/tex]
Part 4) The difference between the lengths of the trails is 2 kilometers
The statement is false
Because
The difference is equal to
[tex]24-18=6\ km[/tex]
Part 5) The difference between the lengths of the trails is 6 kilometers
The statement is true
Because
The difference is equal to
[tex]24-18=6\ km[/tex]
Answer:
2 thirds of the trails are longer than 5 Km
Step-by-step explanation:
