Which of these triangles are definitely right triangles? Explain how you know. (Note that not all triangles are drawn to scale.)

5 triangles labeled A, B, C, D, E. Side lengths for A are: 9, 12, 14. Side lengths for B are: 10, square root 50, square root 50. Side lengths for C are: 16,30,35. Side lengths for D are: 10, 10 point 5, 14 point 5. Side lengths for E are: 4, square root 3, square root 13. 

In each part, \(a\) and \(b\) represent the length (in units) of a leg of a right triangle, and \(c\) represents the length of its hypotenuse. Find the unknown length, given the other two lengths.

1. \(a=12, b=5, c={?}\)

2. \(a={?}, b=21, c=29\)

Andre makes a trip to Mexico. He exchanges some dollars for pesos at a rate of 20 pesos per dollar. While in Mexico, he spends 9,000 pesos. When he returns, he exchanges his pesos for dollars (still at 20 pesos per dollar). He gets back \(\frac{1}{10}\) the amount he started with. Find how many dollars Andre exchanges for pesos and explain your reasoning. If you get stuck, try writing an equation representing Andre’s trip using a variable for the number of dollars he exchanges.