Problema Solution
The distance from Chicago to Cleveland to Cincinnati and back to Chicago is 900 miles. The distance from Chicago to Cleveland is 50 miles more than the distance from Cincinnati to Chicago, and the distance from Cleveland to Cincinnati is 50 miles less than the distance from Cincinnati to Chicago. Find each distance and classify the triangle formed by the three cities.
Answer provided by our tutors
the 3 cities forma a triangle
lets denote the sides of the triangle by
Chicago to Cleveland distance with a
Cleveland to Cincinnati distance with b
Cincinnati to Chicago distance with c
the distance from Chicago to Cleveland to Cincinnati and back to Chicago is 900 miles
a + b + c = 900
the distance from Chicago to Cleveland is 50 miles more than the distance from Cincinnati to Chicago
a = 50 + c
the distance from Cleveland to Cincinnati is 50 miles less than the distance from Cincinnati to Chicago
b = c - 50
plug a = 50 + c and b = c - 50 into a + b + c = 900 we get
50 + c + c - 50 + c = 900
3c = 900
c = 300 miles
a = 50 +300 = 350 miles
b = 300 - 50 = 250 miles
The distance from Chicago to Cleveland is 350 miles.
The distance from Cleveland to Cincinnati is 250 miles.
The distance from Cincinnati to Chicago is 300 miles.