3. choose the correct answer.
a = 3.5 cm, b = √18 cm, c = 6 cm
the triangle is a(n) ____ triangle.
options: acute, obtuse, right

Question

Accepted Answer

# Explanation:
## Step1: Recall the triangle type rule
For a triangle with sides $a$, $b$, $c$ (where $c$ is the longest side), we use the Pythagorean theorem and its extensions. If $a^{2}+b^{2}=c^{2}$, it's a right triangle. If $a^{2}+b^{2}>c^{2}$, it's an acute triangle. If $a^{2}+b^{2}<c^{2}$, it's an obtuse triangle. Here, $c = 6$ is the longest side (since $3.5=\sqrt{12.25}$, $\sqrt{18}\approx4.24$, and $6=\sqrt{36}$).
## Step2: Calculate $a^{2}+b^{2}$
$a^{2}=(3.5)^{2}=12.25$, $b^{2}=(\sqrt{18})^{2}=18$. So $a^{2}+b^{2}=12.25 + 18=30.25$.
## Step3: Calculate $c^{2}$
$c^{2}=6^{2}=36$.
## Step4: Compare $a^{2}+b^{2}$ and $c^{2}$
Since $30.25<36$ (i.e., $a^{2}+b^{2}<c^{2}$), the triangle is obtuse.
# Answer: obtuse

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the triangle type rule

Step2: Calculate \(a^{2}+b^{2}\)

Step3: Calculate \(c^{2}\)

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Answer: