A commuter airline files a new route between two cities that are 400
kilometers apart. One of the two cities is 200 kilometers from a third
city. The other one of the two cities is 300 kilometers from the third
city. Do the paths between the three cities form a right triangle?
Prove that your answer is correct.

For a right triangle to be formed, the Pythagorean Theorem (a2+b2=c2, with a and b being the legs that form the right angle, and c being the hypotenuse) needs to apply correctly to the distances. In a right triangle, the longest distance is always the hypotenuse, or the slanted side that doesn't touch the right angle. The question is to suggest that the hypotenuse is 400 km. long and the legs being 200 km. and 300 km. long respectively. So, to solve this, all we have to do is plug these distances into the Pythagorean Theorem and see if it comes out correct. When plugged in, the equation should be 2002+3002=4002. Then, you solve! It should go like this: 2002+3002=4002, then 40,000+90,000=160000, then add the numbers on the left side to get 130,000=160,000, but, hang on a second. 130,000 does not equal 160,000. This means that the Pythagorean Theorem does not work with the proposed right triangle, which means that the paths between the three cities do NOT form a right triangle!

eudora eudora · Answer 2 · 2022-02-17T13:56:14+01:00

Paths between the three cities do not form a right triangle.

Pythagoras theorem,

"In a right angle triangle, square of the hypotenuse is equal to the sum of squares of the other two sides"

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Given in the question,

A commuter airline flies between two cities A and C which are 400 km apart.
Third city at B is 200 km apart from city A.
And distance between B and C is 300 km.

If ABC is a right triangle, sides of the triangle will follow Pythagoras theorem.

AC² = AB² + BC² [By Pythagoras theorem]

(400)² = (200)² + (300)²

160000 = 40000 + 90000

160000 = 130000

But 160000 ≠ 130000.

Therefore, ΔABC is not a right angle triangle.

Learn more about the use of Pythagoras theorem here,

https://brainly.com/question/12306722?referrer=searchResults