Question

Determine if a triangle can have the given side lengths. If yes, which type of triangle is formed by the side lengths. Choose the correct answer for both rows of the table. HELP GODDD PLZ PLZ PLZ HELP

Answer 1

B and H.

Explanation:

By the triangle inequality, any two sides of a triangle must be greater than the remaining side.

Triangle 1)

The side lengths are 9, 40, and 41.

We only need to check the two smaller sides. 9 + 40 = 49 which is indeed greater than 41. Therefore, this is indeed a triangle.

Remember that if:

`c^2=a^2+b^2`

We have a right triangle.

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

We have an obtuse triangle.

And if:

`c^2<a^2+b^2`

We have an acute triangle.

In all of these, c is the longest side.

Therefore, we will substitute 41 for c and 9 and 40 for the others:

`41^2\text{ }?\text{ }40^2+9^2`

Evaluate:

`1681=1681`

Since the two values are equivalent, the first triangle is a right triangle.

Triangle 2)

Again, adding up the two smaller sides gives that 8 + 10 = 18.

However, 18 is less than 21, so it does not satisfy the triangle inequality.

Therefore, the given side lengths cannot form a triangle.