Two hallways, one 8 feet wide and the other 6 feet wide, meet at right angles. Determine the length of the longest ladder that can be carried horizontally from one hallway into the other.
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To determine the length of the longest ladder that can be carried horizontally from one hallway into the other, we need to find the length of the hypotenuse of a right triangle formed by the two hallways.
In this case, the two hallways act as the legs of the right triangle and the longest ladder acts as the hypotenuse. We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's label the width of the first hallway as A (8 feet) and the width of the second hallway as B (6 feet). The length of the longest ladder, which is the hypotenuse, will be labeled C.
Now, we can apply the Pythagorean theorem:
C^2 = A^2 + B^2
Substituting the values:
C^2 = 8^2 + 6^2
C^2 = 64 + 36
C^2 = 100
Taking the square root of both sides:
C = √100
C = 10 feet
Therefore, the length of the longest ladder that can be carried horizontally from one hallway into the other is 10 feet.