Question

An office has the following dimensions: 12 ft long,

and 8 ft high. The security system will focus an infrared
beam from the top left corner of the ceiling down to the
lower right corner of the floor. What is the length of the
infrared beam?

Answer 1

To find the length of the infrared beam, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse represents the length of the infrared beam, while the other two sides are the height and length of the office.

Height of the office = 8 ft
Length of the office = 12 ft

Using the Pythagorean theorem:

Length of the infrared beam = √(Height^2 + Length^2)
Length of the infrared beam = √(8^2 + 12^2)
Length of the infrared beam = √(64 + 144)
Length of the infrared beam = √208
Length of the infrared beam ≈ 14.42 ft (rounded to two decimal places)

Therefore, the length of the infrared beam is approximately 14.42 feet.