An architectis desining a house in which a 104-square-foot room and a 130-square-foot room share a wall . what is the greatest possible integer length of the shared wall?

Question

asked Jan 8, 2019 152k views

1 Answer

Mats Wichmann · Answer 1 · 2019-01-14T13:14:19+0000

In my experience architects generally avoid number theory.

Let's called the shared wall

. The area is width times height, so the other walls are
104/s

and

. We want the biggest s that gives integer quotients; that would be the greatest common factor of 104 and 130.

104 = 2^3 13^1

Greatest common factor and largest shared wall,

w = 2 * 13 = 26

That's None of the Above, though 26x4 and 26x5 rooms are pretty goofy, probably why architects don't worry about number theory.