Advanced and Real-World Applications

1) Which equation represents all Pythagorean triples?

X² + y² = 2z²

X² + y² = (x+y)²

X² + y² = z²

X² - y² = z²

2) If a 3 mod 4 and b 4 mod 4, then (a, b, c) is:

Always primitive

Possibly part of a primitive triple

Never primitive

Undefined

3) Which is a Pythagorean triple?

(15, 20, 25)

(7, 24, 25)

(8, 9, 13)

Both (15, 20, 25) & (7, 24, 25)

4) Which triple connects to the equation of a circle x² + y² = r²?

(3, 4, 5)

(5, 12, 13)

(8, 15, 17)

All of the above

5) Which triple relates to a right triangle with area 210?

(14, 48, 50)

(18, 24, 30)

(20, 21, 29)

(7, 24, 25)

6) The distance between (0, 0) and (9, 40) is:

43

42

41

40

7) Which set corresponds to the primitive triple using m = 4, n = 1?

(8, 15, 17)

(15, 20, 25)

(7, 24, 25)

(20, 21, 29)

8) If z² - y² = x², and (x, y, z) = (12, 35, 37), then the relation is:

Invalid

Valid

Only approximate

None

9) Which set does not satisfy the Pythagorean theorem?

(9, 40, 41)

(11, 60, 61)

(16, 30, 34)

(10, 25, 27)

10) An engineer designs a ramp that rises 12 ft over 35 ft of horizontal distance. The length of the ramp is:

36 ft

37 ft

38 ft

39 ft