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

1 Answer
Truong-Son N.
Nov 13, 2015

If you note that #81# is a perfect square, you can say that for a real square shape:

#sqrt(81) = 9#

Furthermore, since you have a square, the diagonal, which forms a hypotenuse, creates a #45^@-45^@-90^@# triangle.

So, we would expect the hypotenuse to be #9sqrt2# since the general relationship for this special type of triangle is:

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

Let's show that #c = 9sqrt2# using the Pythagorean Theorem.

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

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

#= sqrt(81 + 81)#

#= sqrt(2*81)#

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

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