If a room is 50 feet by 100 feet, what is the length of the diagonal?

To find the length of the diagonal in a rectangular room, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides.

In this scenario, the sides of the rectangle are 50 feet and 100 feet. By applying the Pythagorean theorem:

1. Square the lengths of the two sides:

• 50-feet side: ( 50^2 = 2500 )

• 100-feet side: ( 100^2 = 10000 )

2. Add these two results together:

• ( 2500 + 10000 = 12500 )

3. Take the square root of that sum to find the diagonal:

• ( \sqrt{12500} )

Calculating this gives approximately 111.8 feet, which is closest to 112 feet when rounded off. This confirms that the correct length of the diagonal is 112 feet, aligning with option C.

Understanding how to use the Pythagorean theorem in practical applications, such as determining lengths in