# The area of a square is 81 square centimeters. What is the length of the diagonal?

##### 1 Answer

Nov 13, 2015

If you note that

#sqrt(81) = 9#

Furthermore, since you have a square, the diagonal, which forms a hypotenuse, creates a

So, we would expect the hypotenuse to be

#a = n# #b = n# #c = nsqrt2#

Let's show that

#c = sqrt(a^2 + b^2)#

#= sqrt(9^2 + 9^2)#

#= sqrt(81 + 81)#

#= sqrt(2*81)#

#= color(blue)(9sqrt2 " cm"#