Answer:
b. 40
Explanation:
You want the missing leg length in a right triangle with one side of length 9 and the hypotenuse of length 41.
Reasonableness
The missing side of any triangle will be between the sum and difference of the other two side lengths.
c-a < b < c+a
32 < b < 50
In a right triangle, every side length is less than the length of the hypotenuse:
b < c
32 < b < 41
There is only one answer choice in this range: b = 40.
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Additional comment
You can make use of your knowledge of Pythagorean triples. One of them is {9, 40, 41}, which tells you that b=40.
Or, you can use the Pythagorean theorem to compute b:
a² +b² = c²
9² +b² = 41²
b² = 1681 -81 = 1600
b = √1600 = 40
For any odd integer, there is a Pythagorean triple with sides 1 unit apart such that those longer side lengths are about half of the square of that odd integer:
9² = 81 = 40+41
so {9, 40, 41} is a Pythagorean triple.
The simplest of these is ...
3² = 9 = 4+5 ⇒ {3, 4, 5} is a Pythagorean triple.