For a room measuring 12' by 9', what is the length of a diagonal line drawn between two corners?

To calculate the length of the diagonal line drawn between two corners of a rectangular room measuring 12 feet by 9 feet, you can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal, in this case) is equal to the sum of the squares of the lengths of the other two sides.

In this scenario, you have:

• One side measuring 12 feet (length).

• Another side measuring 9 feet (width).

Applying the Pythagorean theorem:

1. Square the lengths of both sides:

( 12^2 = 144 )

( 9^2 = 81 )

2. Add the two squared values:

( 144 + 81 = 225 )

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

( \sqrt{225} = 15 )

Thus, the length of the diagonal line drawn between two corners of the room is 15 feet. This is why the correct answer is identified as 15 feet.