If the length of the long wall is 12 feet and the length of the diagonal wall is 13 feet, how long is the shorter wall?

The shorter wall is 5 feet long.

Step-by-step explanation:

This problem can be solved by visualizing the the long wall, short wall, and diagonal wall as a right triangle.

After doing so, the problem can be solved by utilizing the Pythagorean Theorem, which states that in a right triangle, the sides must be equivalent to a^2 + b^2 = c^2, with a b and c being the actual lengths of the sides of the triangle.

To begin, you would create the equation a^2 + 12^2 = 13^2 (c always indicates the hypotenuse, but a and b are interchangeable for the remaining sides).

Then, you would find the square of 12 and 13, which would be 144 and 169, respectively. Thus, a^2 + 144 = 169.

Next, you would get a^2 by itself on the left side in order to solve for it by subtracting 144 from both sides, which grants the equation a^2 = 25.

Finally, after finding the square root of both sides, you get the final answer of a = 5. Thus, the shorter wall is 5 feet long.

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

irrational, cannot