Question

Aaron and Mark get off a roller coaster ride at an amusement park. Next, they head for the bumper car ride. Each boy takes a different path. Aaron's path is shown in red; Mark's path is shown in blue.A right triangle whose side measures two hundred and whose other side measures two hundred fifty.

a. What is the length of Aaron's path? Show and explain your work.

b. What is the length of Mark's path? Show and explain your work.

c. Which boy had a longer walk? How much longer? Show and explain your work.

Answer 1

picture here can you please help me with this formula thanks.

Answer 2

Aaron's path is shown in red. His path consists of two straight lines. We know those two sides are 200 yd and 250 yd, so his total path is 200 yd + 250 yd = 450 yd.

Mark takes a straight path. His path is the hypotenuse of the right triangle. For any right triangle, the sum of the squares of the two legs is equal to the sum of the hypotenuse. In other words, for a right triangle with legs a and b and hypotenuse c:
\[a^2 + b^2 = c^2\]So Mark's path is equal to:
\[\sqrt{a^2 + b^2}=\sqrt{200^2 + 250^2} \approx 320.2 yd\]

Aaron's path is clearly longer, by 450-320.2=129.8 yd