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 can use the Pythagorean Theorem.
Step 1: Visualize the problem.
Imagine a right triangle formed by the two hallways. The width of one hallway is the base of the triangle, the width of the other hallway is the height, and the length of the ladder is the hypotenuse.
Step 2: Apply the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the formula is:
ladder^2 = width1^2 + width2^2
Step 3: Plug in the values.
In this case, the width of one hallway is 8 feet and the width of the other hallway is 6 feet. Let's plug these values into the formula:
ladder^2 = 8^2 + 6^2
Step 4: Simplify and solve for the ladder's length.
Calculating the right side of the equation:
ladder^2 = 64 + 36
ladder^2 = 100
To find the ladder's length, we need to take the square root of both sides:
ladder = √100
ladder = 10 feet
Therefore, the length of the longest ladder that can be carried horizontally from one hallway into the other is 10 feet.