Answer: Shortest diagonal = 39 inches
Step-by-step explanation:
We consider ΔAOD, from the figure mentioned below:
To get the diagonal we use the pythagorus theorem,
[tex]AO^2+OD^2=AD^2\\\\AO^2+40^2=41^2\\\\AO^2+1600=1681\\\\AO^2=1681-1600\\\\AO^2=81\\\\AO=\sqrt{81}\\\\AO=9[/tex]
Similarly,
We consider ΔCOD,
By Pythagorus theorem,
[tex]CD^2=CO^2+DO^2\\\\50^2=CO^2+40^2\\\\2500=CO^2+1600\\\\2500-1600=CO^2\\\\900=CO^2\\\\\sqrt{900}=CO\\30=CO[/tex]
So, by adding both two i.e.
[tex]\text{Shortest diagonal of kite }=AC=AO+CO=9+30=39\text{ inches }[/tex]
