Answer:
Step-by-step explanation:
The Pythagorean theorem is expressed as
Hypotenuse² = opposite side² + adjacent side²
If the distances of the routes given are Pythagorean triples, then they obey the Pythagorean theorem hence, they would form a right angle triangle.
1) for the bus routes between stop A, B and C,
13² = 12² + 5²
169 = 144 + 25 = 169
A Pythagorean triple is formed hence, stop A, B and C form a right angle triangle.
2) for the bus routes between stop C, E and E,
22² = 14² + 18²
484 = 196 + 324 = 520
A Pythagorean triple is not formed hence, stop C, E and E do not form a right angle triangle.
3) 25² = 9² + HJ²
625 = 81 + HJ²
HJ² = 625 - 81 = 544
HJ = √544 = 23.32
4) EG² = 15² + 8²
EG² = 225 + 64
EG² = 289
EG = √289 = 17
