Show that the area of a right-angled triangle with all side lengths integers is an
integer divisible by 6.
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1 Answers
46Simple, remember what are pythagorean triplets?? 3,4,5 8,15,17 then 10,24,26 etc. They all form sides of a right angled triangle. Now, pythagorean triplets are of the form (2n, n^2-1, n^2+1). Now these are also the perp, base and hypotenuse of a right angled triangle respectively.Area=1/2*base*height. so, area=1/2*2n*(n^2-1)=n(n^2-1) which is divisible by 6 for any integer value of n. Check to see
