Question

What type of triangle has side lengths of 4√5, √145 and 19?

Answer 1

a, b, c - side lengths (a ≤ b ≤ c)

If $a^2+b^2 < c^2$, then is Obtuse triangle.

If $a^2+b^2=c^2$, then is Right triangle.

If $a^2+b^2 > c^2$, then Acute triangle.

$a=4\sqrt5,\ b=\sqrt{145},\ c=19\to a < b < c$

Check to see if the sum of the first two sides is greater than the third.

$a+b=4\sqrt5+\sqrt{145}\approx9+12=21 > 19=c\\\\CORRECT$

$a\neq b\neq c\neq a$, therefore is Scalene triangle.

$a^2=(4\sqrt5)^2=4^2(\sqrt5)^2=16(5)=80\\\\b^2=(\sqrt{145})^2=145\\\\c^2=19^2=361\\\\a^2+b^2=80+145=225 < 361=c^2\\\\a^2+b^2 < c^2$

It's Obtuse triangle.