Question

Which best describes a triangle with side lengths of 6 inches 8 inches and 9 inches?

A). ambiguously defined
B).non-existent
C).a unique,acute triangle
D).a unique,right triangle

Answer 1

The option that best describes a triangle with side lengths of 6 inches 8 inches and 9 inches is:

C) a unique , acute triangle

Explanation:

We know that with the help of given three side lengths always a unique triangle is possible.

Pythagorean Theorem for acute angles states that:

If c is the longest side of a triangle and a and b are other two sides of a triangle.

Then,

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

Here the three sides of a triangle are:

6 inches 8 inches and 9 inches.

i.e. the longest side i.e. c = 9 inches.

Also, let a=6 inches and b=8 inches.

and

`9^2<6^2+8^2\\\\81<36+64\\\\81<100`

Hence, the triangle is a acute triangle.

Answer 2

The correct answer for this question is this one: "C).a unique,acute triangle"

The statement that best describes a triangle with side lengths of 6 inches 8 inches and 9 inches is that it is a unique,acute triangle
Hope this helps answer your question and have a nice day ahead.