Scooter and Kayla are building a chicken coop in their back yard. The coop will be in the shape of a right triangle. One of the sides will be the wall of the garage. They have $11$ feet of fencing, and one leg will be $4$ feet long.

1. If the garage forms the hypotenuse of the triangle, how long will the other leg be? How long will the hypotenuse be?

   Hint (a):

   If the garage forms the hypotenuse, then the fencing will make up the legs of the triangle.
   If there is $11$ feet of fencing, and one side of the triangle is $4$ feet long, what is the length of the other leg?

   Help (a):

   The other leg will be $7$ feet long. To find the length of the hypotenuse use the Pythagorean theorem.

   More help (a):

   $4^2 + 7^2 = x^2$

2. If the garage wall is one leg of the triangle, how long will the hypotenuse be? How long will the leg along the garage be?

   Hint (b):

   If the garage wall is a leg of the triangle instead of the hypotenuse, then its value cannot be greater than $7$.
   The side with a value of $7$ is, therefore, the new hypotenuse.

   Answer (b):

   The leg along the garage will be $5.74$ ft.

3. What is the area of each chicken coop in parts (a) and (b)?

   Hint (c):

   The new Pythagorean equation is: $4^2 + x^2 = 7^2$

   Help (c):

   To find each area, multiply the two legs (since they are perpendicular to each other and therefore form the base and the height) and divide that product by $2$.

   Partial Answer (c):

   The area for (a) is $14$ ft^{$^{2}$}.
   What is the area for (b)?