   SEARCH HOME Math Central Quandaries & Queries  Question from FRANK, a parent: WHAT IS THE LENGTH OF ONE SIDE OF A SQUARE WITH A DIAGONAL OF LENGTH 2 TO THE HALF POWER Hi Frank.

Pythagoras' Theorem says that a2 + b2 = h2 for any right triangle where h is the length of the hypotenuse and a and b are the lengths of the legs. For a square with a diagonal drawn through it, h is the diagonal and a and b are the legs. In a square of course, a = b, so you
have

2a2 = h22

where a is the length of the side of the square and h is the diagonal length.

Now you can solve for the length a (because that is what you want to know):

a2 = h2 / 2
a = sqrt( h2 / 2)
a = h / sqrt(2)

If you know the length h (you said it is 2 to the one half power, which is the same as sqrt(2)) then you can just substitute that value in for h to find the value of a:

a = sqrt(2) / sqrt(2) = 1.

So the answer is simply 1 unit.

Cheers,
Steve La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.