### Home > MC2 > Chapter 10 > Lesson 10.1.1 > Problem10-10

10-10.

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?

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?

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

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

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?

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.

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

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

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

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 $2$.

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