Question

Can three segments with length 4 cm 6 cm and 11 cm be assembled to form an acute triangle a right triangle or an obtuse triangle?

Answer 1

Is an obtuse triangle

Explanation:

Let

c ----> the greater side of triangle

a and b are the other two sides of triangle

we know that

If
`c^2=a^2+b^2` ----> then we have a right triangle (Pythagorean Theorem)

If
`c^2>a^2+b^2` ----> then we have an obtuse triangle

If
`c^2<a^2+b^2` ----> then we have an acute triangle

we have

`c=11\ cm\\a=4\ cm\\b=6\ cm`

substitute the given values

`c^2=11^2=121`

`a^2+b^2=4^2+6^2=52`

so

`c^2> a^2+b^2`

therefore

Is an obtuse triangle