Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

# The annual Cheese Rolling happens in May at Gloucestershire, England. As the name suggests, large, 7-9 pound wheels of cheese are rolled down a steep hill, and people chase after them. The first person to the bottom wins cheese. Renaldo wants to go to the Cheese Rolling: He plans to leave from Atlanta and fly into London ( 4281 miles). On the return, he will fly back from London to New York City ( 3470 miles) to visit his aunt. Then Renaldo heads back to Atlanta. Atlanta, New York City, and London do not lie on the same line. Find the range of the total distance Renaldo could travel on his trip.

Solution

Verified
Step 1
1 of 3
According to the Triangle Inequality Theorem the sum of any two sides of a triangle must be greater than the measure of the third side. If $a, b$ are two known sides and $x$ is the unknown third side, we have (assume that $a\leq b$): \begin{align*} \begin{cases} a+b>x\\ a+x>b\\ b+x>a \end{cases}\\ \begin{cases} a+b>x\\ x>b-a\\ x>a-b \end{cases}\\ \end{align*} As $a\leq b$ we can write: \begin{align*} \begin{cases} a+b>x\\ x>b-a\\ \end{cases}\\ or\\ b-a

## Recommended textbook solutions

#### Holt Geometry Homework and Practice Workbook

1st EditionISBN: 9780030780875 (1 more)Rinehart, Winston and Holt
834 solutions

#### Geometry

1st EditionISBN: 9780076639298Carter, Cuevas, Cummins, Day, Malloy
4,577 solutions

#### enVision Geometry

1st EditionISBN: 9780328931583 (3 more)Al Cuoco
2,702 solutions

#### Big Ideas Math Geometry: A Common Core Curriculum

1st EditionISBN: 9781608408399 (1 more)Boswell, Larson
4,072 solutions