Question

What type of triangle has side lengths 2, √11, and √15? please leave details as to how you got to your conclusion im confused

Answer 1

right triangle.

Explanation:

The given length of the three sides of the triangle are

`2,√(11),√(15)`

We will now check whether these three numbers are Pythagorean triple or not. If it is a Pythagorean triple then the triangle will be a right triangle.

Pythagorean triple:- If the sum of square of any two sides is equal to the square of the third side then the lengths are Pythagorean triple and the triangle is a right triangle.

Now, we do the below operation:

`2^2+(√(11))^2\\\\=4+11\\\\=15`

Now, let us square the third side

`(√(15))^2\\\\=15`

Since, we got both values equal. Hence, the length of sides are Pythagorean triple.

And therefore, the triangle is right triangle.

Answer 2

Let "a", "b" and "с" be sides of the triangle ("с" is the longest side). The triangle will be:
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²

We have a=2, b=√11 and c=√15

2² + (√11)² = 4 + 11 = 15
and
(√15)² = 15

15 = 15 ⇒ right triangle.

Hope this helps.