Which is best estimate for the length of the short leg a if the hypotenuses c is about 10 cm 15 points!! A)4 cm B)5 cm C)6 cm D)8 cm E)none of the above

Answer:A)4Step-by-step explanation:Assuming all edges are integral valuesThe most basic right angles triangle with integral edges is(3,4,5)as it obeys pythogores theoremwhich is [tex]a^{2}+ b^{2} =c^{2} \\\text{where c is the hypotenuse}\\\text{and a and b are the other side}[/tex][tex]3^{2} +4^{2} =5^{2}[/tex]Now, double each edge,it will still remain a right angled triangle since it will still obey pythogores theoremso the edges are (4,6,10)⇒4 cm is the short leg of a integral right triangle with hypotenuse 10 cm