ANSWER
C. 80
EXPLANATION
The longer diagonal is serving as the hypotenuse of the right triangles.
Let the longer side of the kite be x cm.
Then, from the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.
This means that,
[tex] {x}^{2} + {60}^{2} = {100}^{2} [/tex]
[tex] {x}^{2} + 3600 = 10000[/tex]
[tex] {x}^{2} = 10000 - 3600[/tex]
[tex] {x}^{2} = 6400[/tex]
[tex]x = \sqrt{6400} [/tex]
[tex]x = 80cm[/tex]
