Final answer:
To find a Pythagorean triplet whose smallest member is 9, substitute 9 for one of the legs in the Pythagorean theorem equation. One possible solution is (9, 40, 41).
Step-by-step explanation:
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). To find a Pythagorean triplet whose smallest member is 9, we can start by substituting 9 for the value of one of the legs (a) in the equation. Let's use the equation a^2 + b^2 = c^2 and substitute a = 9:
9^2 + b^2 = c^2
Simplifying the equation, we get:
81 + b^2 = c^2
Now, we need to find two values for b and c that satisfy this equation. One possible solution is b = 40 and c = 41. Thus, the Pythagorean triplet with a smallest member of 9 is (9, 40, 41).