two hallways meet at a right angle, one is 8ft and the other 6ft wide. find the lenth of the longest beam?

Question

that can turn the corner where the hallways intersect

Answer 1

Sounds like a calculus question. let theta = angle formed between the inside wall of the 8ft hallway and the beam. The maximum length of the beam will be 8/sin(theta)+6/cos(theta). Find the derivative of this function and set it equal to zero. That will give you the theta that gives the maximum length. Plug that theta into the beam length equation to find your answer. I'm rusty in calculus so I won't even try to find the derivative.

Ok, I did a little more searching, theta that gives maximum length is 47.24 degrees this translates into 19.73' if you neglect the thickness of the beam and consider it a line.

Answer 2

Pythagorean Theorem

8^2+6^2=x^2
64+36=x^2
x=10

Answer 3

This is an example of the Pythagorean Theoram.
a^2 + b^2 = c^2

In this case, 8 = a, 6 = b.

8^2 + 6^2 = c^2.

64 = 36 = 100.

sqrt of 100 = 10.

c= 10.