Question 230563
If the area of a square is 169 cm2, what is the length of the diagonal?


Step 1.  The area of a square with side {{{A=s^2=169}}} square cm.


Step 2.  Take the square root to get {{{s=sqrt(169)=13}}} cm.


Step 3.  The diagonal splits the square into two right triangles.  As a result, we can use the Pythagorean Theorem which says that the sum of the square of the legs is equal to the hypotenuse.  The legs are the sides of the square given as s and let d be the diagonal.  Then,


{{{d^2=s^2+s^2}}}


{{{d^2=2s^2}}}


Take the square root to both sides of the equation


{{{sqrt(d^2)=sqrt(2s^2)}}}


{{{d=s*sqrt(2)}}}


{{{d=13*sqrt(2)}}}


{{{d=18.38}}}


Step 4.  ANSWER:  The diagonal {{{d=13*sqrt(2)}}} cm or {{{d=18.38}}} cm


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J