In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 9 feet of fence for the shortest side and 15 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
a) 12 feet
b) 16 feet
c) 36 feet
d) 38 feet
To find the length of the third side, we can use the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the lengths of the two sides and c is the length of the hypotenuse (longest side).
In this case, a = 9 feet and c = 15 feet.
Doing the calculation, we have: 9^2 + b^2 = 15^2
Simplifying, we get: 81 + b^2 = 225
Subtracting 81 from both sides, we have: b^2 = 144
Taking the square root of both sides, we get: b = 12
So, the length of the third side is 12 feet.
To find the total length of the fencing needed, we add the lengths of all three sides together: 9 + 12 + 15 = 36 feet.
Therefore, the correct answer is c) 36 feet.