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=√(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+√(145)\approx9+12=21 > 19=c\\\\CORRECT`

`a\\eq b\\eq c\\eq a`, therefore is Scalene triangle.

`a^2=(4\sqrt5)^2=4^2(\sqrt5)^2=16(5)=80\\\\b^2=(√(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.