Question

Last one!! Please help! show work too thank you guys

Answer 1

Let's call the sides in order a,b,c

A right triangle satisfies
`a^2+b^2=c^2`

An obtuse triangle has a longer long side, so that's
`a^2+b^2 < c^2`

An actute triangle is
`a^2+b^2>c^2`

We sort, square, add, and compare

4.

11,60,61

`11^2 + 60^2 = 121+3600 = 3721`

`61^2 = 3721 \quad\checkmark`

Answer: Right Triangle

5.

4,5,7

`4^2+5^2= 16 +25=41`

`7^2=49`

That's a bigger c, so

Answer: obtuse triangle

6.

7,19,25

`7^2+19^2=49+361=410`

`25^2 = 625`

Answer: obtuse triangle