Answer:
1) 12 (option b)
2) 41, 9, 40 (option a)
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
1) Let the unknown leg be x cm long. Thus,
5² + x² = 13²
Simplify and solve.
25 + x² = 169
x² = 144
x = 12
2) Apply the Pythagorean Theorem.
9² + 40² = 41² = 81 + 1600 = 1681
1681 = 1681
a is true.
Just in case, let's check the other options.
5² + 8² = 9² = 25 + 64 = 81
89 = 81, false
b is false
10² + 11² = 12² = 100 + 121 = 144
221 = 144, false
c is false
3² + 4² = 6² = 9 + 16 = 36
25 = 36, false
d is false
Thus, a is the answer.
