Answer
No
Work Step by Step
(5,6,7)
Using Heron's formula if three sides of a triangle have length a,b,c then area A of a triangle is
A = $\sqrt s(s-a)(s-b)(s-c)$
where s = $\frac{a+b+c}{2}$
Lets take a=5 b=6 and c=7
s = $\frac{5+6+7}{2}$
= 9
A = $\sqrt 9(9-5)(9-6)(9-7)$
=$\sqrt 9 * 4*3*2$
= 6$\sqrt 6$ = 14.69
If a,b,c be the integer length of the sides of a triangle . If the area of the triangle is also a integer then (a,b,c) is known as a heron triplet.
Since A = 14.69 not a integer
(a,b,c) = (5,6,7) integer
Therefore the triplet is not a heron triplet.
