Answer:
B. 11.4 mi
C. 2.6 mi
Step-by-step explanation:
You can find the length of the diagonal using the Pythagorean theorem.
Where a and b are sides of a triangle, the hypotenuse c (the diagonal) is
[tex]c^2 = a^2 + b^2\\c = \sqrt{a^2+b^2}[/tex]
In our problem, the sides a and b are the lengths FG and GH.
The diagonal is FH. Thus:
[tex]FH = \sqrt{FG^2+GH^2}[/tex]
FG = 5 mi
GH = 4 mi
[tex]FH = \sqrt{5^2+4^2}=\sqrt{25+16}=\sqrt{41}=6.40312424[/tex]
Since we're rounding to the nearest tenth of a mile, we can say that the length of the proposed road FH is 6.4 miles.
The entire distance from EH would be EF + FH.
Since EF is 5 miles, the entire distance EH using the proposed road would be:
EH = EF + FH
EH = 5 + 6.4
EH = 11.4
Answer: 11.4 miles
To answer the last question, we need the distance using existing rods.
The distance EH using existing roads is EG + GH.
EG = 10 mi
GH = 4 mi
EH = 10 + 4 = 14
Using existing roads, the distance is 14 miles.
To find the difference, we'll just subtract the 2 values.
14 - 11.4 = 2.6
Answer: 2.6 miles
