I have another Pythagorean theorem: word problem that has stumped me for the last time. The floor of storage unit is 12 meters long and 9 meters wide. What is the distance between two opposite corners of the floor? Thank you so much!

So you just want the hypotenuse of a triangle with sides 12 and 9, so

h^2 = 12^2 + 9^2 = 225
take √225 and you have it.

(after doing about 5000 of these, you will recognize the simplest right-angled triangle
of 3-4-5 units has been multiplied by 3 to get yours)

Thank you so much. Now I see what I did wrong. I'm such an idiot.

To find the distance between two opposite corners of the floor, you can use the Pythagorean theorem.

Step 1: Identify the two sides of the floor that will form a right triangle. In this case, the length (12 meters) and width (9 meters) of the floor will form the two sides of the right triangle.

Step 2: Use the Pythagorean theorem formula, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Step 3: Apply the formula. Let's denote the length as a, the width as b, and the hypotenuse as c. In this case, a = 12 meters and b = 9 meters. We will solve for c.

The Pythagorean theorem formula is:

a^2 + b^2 = c^2

By substituting the values, we have:

12^2 + 9^2 = c^2

Step 4: Simplify the equation:

144 + 81 = c^2

225 = c^2

Step 5: Take the square root of both sides to solve for c:

c = sqrt(225)
c = 15 meters

Therefore, the distance between two opposite corners of the floor is 15 meters.

To find the distance between two opposite corners of the floor, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the length and width of the floor form the two sides of a right triangle, and the distance between the two opposite corners is the hypotenuse.

So, let's label the length as 'a' (12 meters) and the width as 'b' (9 meters). We can use these values to calculate the distance between two opposite corners.

The Pythagorean theorem equation is:

c² = a² + b²

where c represents the length of the hypotenuse.

Plugging in the values:

c² = (12²) + (9²)
c² = 144 + 81
c² = 225

To find the value of c, we need to take the square root of 225:

c = √225
c = 15 meters

Therefore, the distance between two opposite corners of the floor is 15 meters.