In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 16 feet of fence for the shortest side and 20 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen?
a 8 feet
b 12 feet
c 36 feet
d 48 feet
To find the length of the hypotenuse (longest side) of the triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
So, in this case, we have:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
We are given that one side is 16 feet and another side is 20 feet. Plugging these values into the equation, we have:
c² = 16² + 20²
c² = 256 + 400
c² = 656
c ≈ 25.61 feet (rounding to two decimal places)
Now, to find the total length of the fencing needed, we add up the lengths of all three sides:
16 + 20 + 25.61 ≈ 61.61 feet
So, the correct answer is:
d) 48 feet